--- a/NEWS Wed Apr 25 11:29:55 2012 +0200
+++ b/NEWS Wed Apr 25 14:28:13 2012 +0200
@@ -693,143 +693,143 @@
product_sigma_algebra
Removed constants:
+ conditional_space
distribution -> use distr measure, or distributed predicate
+ image_space
joint_distribution -> use distr measure, or distributed predicate
+ pair_measure_generator
product_prob_space.infprod_algebra -> use PiM
subvimage
- image_space
- conditional_space
- pair_measure_generator
Replacement theorems:
- sigma_algebra.measurable_sigma -> measurable_measure_of
+ finite_additivity_sufficient -> ring_of_sets.countably_additiveI_finite
+ finite_measure.empty_measure -> measure_empty
+ finite_measure.finite_continuity_from_above -> finite_measure.finite_Lim_measure_decseq
+ finite_measure.finite_continuity_from_below -> finite_measure.finite_Lim_measure_incseq
+ finite_measure.finite_measure_countably_subadditive -> finite_measure.finite_measure_subadditive_countably
+ finite_measure.finite_measure_eq -> finite_measure.emeasure_eq_measure
+ finite_measure.finite_measure -> finite_measure.emeasure_finite
+ finite_measure.finite_measure_finite_singleton -> finite_measure.finite_measure_eq_setsum_singleton
+ finite_measure.positive_measure' -> measure_nonneg
+ finite_measure.real_measure -> finite_measure.emeasure_real
+ finite_product_prob_space.finite_measure_times -> finite_product_prob_space.finite_measure_PiM_emb
+ finite_product_sigma_algebra.in_P -> sets_PiM_I_finite
+ finite_product_sigma_algebra.P_empty -> space_PiM_empty, sets_PiM_empty
+ information_space.conditional_entropy_eq -> information_space.conditional_entropy_simple_distributed
+ information_space.conditional_entropy_positive -> information_space.conditional_entropy_nonneg_simple
+ information_space.conditional_mutual_information_eq_mutual_information -> information_space.conditional_mutual_information_eq_mutual_information_simple
+ information_space.conditional_mutual_information_generic_positive -> information_space.conditional_mutual_information_nonneg_simple
+ information_space.conditional_mutual_information_positive -> information_space.conditional_mutual_information_nonneg_simple
+ information_space.entropy_commute -> information_space.entropy_commute_simple
+ information_space.entropy_eq -> information_space.entropy_simple_distributed
+ information_space.entropy_generic_eq -> information_space.entropy_simple_distributed
+ information_space.entropy_positive -> information_space.entropy_nonneg_simple
+ information_space.entropy_uniform_max -> information_space.entropy_uniform
+ information_space.KL_eq_0_imp -> information_space.KL_eq_0_iff_eq
+ information_space.KL_eq_0 -> information_space.KL_same_eq_0
+ information_space.KL_ge_0 -> information_space.KL_nonneg
+ information_space.mutual_information_eq -> information_space.mutual_information_simple_distributed
+ information_space.mutual_information_positive -> information_space.mutual_information_nonneg_simple
+ Int_stable_cuboids -> Int_stable_atLeastAtMost
+ Int_stable_product_algebra_generator -> positive_integral
+ measure_preserving -> equality "distr M N f = N" "f : measurable M N"
measure_space.additive -> emeasure_additive
- measure_space.measure_additive -> plus_emeasure
- measure_space.measure_mono -> emeasure_mono
- measure_space.measure_top -> emeasure_space
- measure_space.measure_compl -> emeasure_compl
- measure_space.measure_Diff -> emeasure_Diff
- measure_space.measure_countable_increasing -> emeasure_countable_increasing
+ measure_space.AE_iff_null_set -> AE_iff_null
+ measure_space.almost_everywhere_def -> eventually_ae_filter
+ measure_space.almost_everywhere_vimage -> AE_distrD
+ measure_space.continuity_from_above -> INF_emeasure_decseq
+ measure_space.continuity_from_above_Lim -> Lim_emeasure_decseq
+ measure_space.continuity_from_below_Lim -> Lim_emeasure_incseq
measure_space.continuity_from_below -> SUP_emeasure_incseq
- measure_space.measure_incseq -> incseq_emeasure
- measure_space.continuity_from_below_Lim -> Lim_emeasure_incseq
+ measure_space_density -> emeasure_density
+ measure_space.density_is_absolutely_continuous -> absolutely_continuousI_density
+ measure_space.integrable_vimage -> integrable_distr
+ measure_space.integral_translated_density -> integral_density
+ measure_space.integral_vimage -> integral_distr
+ measure_space.measure_additive -> plus_emeasure
+ measure_space.measure_compl -> emeasure_compl
+ measure_space.measure_countable_increasing -> emeasure_countable_increasing
+ measure_space.measure_countably_subadditive -> emeasure_subadditive_countably
measure_space.measure_decseq -> decseq_emeasure
- measure_space.continuity_from_above -> INF_emeasure_decseq
- measure_space.measure_insert -> emeasure_insert
- measure_space.measure_setsum -> setsum_emeasure
- measure_space.measure_finite_singleton -> emeasure_eq_setsum_singleton
- finite_additivity_sufficient -> ring_of_sets.countably_additiveI_finite
- measure_space.measure_setsum_split -> setsum_emeasure_cover
- measure_space.measure_subadditive -> subadditive
- measure_space.measure_subadditive_finite -> emeasure_subadditive_finite
+ measure_space.measure_Diff -> emeasure_Diff
+ measure_space.measure_Diff_null_set -> emeasure_Diff_null_set
measure_space.measure_eq_0 -> emeasure_eq_0
measure_space.measure_finitely_subadditive -> emeasure_subadditive_finite
- measure_space.measure_countably_subadditive -> emeasure_subadditive_countably
- measure_space.measure_UN_eq_0 -> emeasure_UN_eq_0
- measure_unique_Int_stable -> measure_eqI_generator_eq
- measure_space.measure_Diff_null_set -> emeasure_Diff_null_set
- measure_space.measure_Un_null_set -> emeasure_Un_null_set
- measure_space.almost_everywhere_def -> eventually_ae_filter
- measure_space.almost_everywhere_vimage -> AE_distrD
+ measure_space.measure_finite_singleton -> emeasure_eq_setsum_singleton
+ measure_space.measure_incseq -> incseq_emeasure
+ measure_space.measure_insert -> emeasure_insert
+ measure_space.measure_mono -> emeasure_mono
+ measure_space.measure_not_negative -> emeasure_not_MInf
+ measure_space.measure_preserving_Int_stable -> measure_eqI_generator_eq
+ measure_space.measure_setsum -> setsum_emeasure
+ measure_space.measure_setsum_split -> setsum_emeasure_cover
measure_space.measure_space_vimage -> emeasure_distr
- measure_space.AE_iff_null_set -> AE_iff_null
- measure_space.real_measure_Union -> measure_Union
- measure_space.real_measure_finite_Union -> measure_finite_Union
- measure_space.real_measure_Diff -> measure_Diff
- measure_space.real_measure_UNION -> measure_UNION
- measure_space.real_measure_subadditive -> measure_subadditive
- measure_space.real_measure_setsum_singleton -> measure_eq_setsum_singleton
- measure_space.real_continuity_from_below -> Lim_measure_incseq
- measure_space.continuity_from_above_Lim -> Lim_emeasure_decseq
+ measure_space.measure_subadditive_finite -> emeasure_subadditive_finite
+ measure_space.measure_subadditive -> subadditive
+ measure_space.measure_top -> emeasure_space
+ measure_space.measure_UN_eq_0 -> emeasure_UN_eq_0
+ measure_space.measure_Un_null_set -> emeasure_Un_null_set
+ measure_space.positive_integral_translated_density -> positive_integral_density
+ measure_space.positive_integral_vimage -> positive_integral_distr
measure_space.real_continuity_from_above -> Lim_measure_decseq
+ measure_space.real_continuity_from_below -> Lim_measure_incseq
measure_space.real_measure_countably_subadditive -> measure_subadditive_countably
- finite_measure.finite_measure -> finite_measure.emeasure_finite
- finite_measure.finite_measure_eq -> finite_measure.emeasure_eq_measure
- finite_measure.positive_measure' -> measure_nonneg
- finite_measure.real_measure -> finite_measure.emeasure_real
- finite_measure.empty_measure -> measure_empty
- finite_measure.finite_measure_countably_subadditive -> finite_measure.finite_measure_subadditive_countably
- finite_measure.finite_measure_finite_singleton -> finite_measure.finite_measure_eq_setsum_singleton
- finite_measure.finite_continuity_from_below -> finite_measure.finite_Lim_measure_incseq
- finite_measure.finite_continuity_from_above -> finite_measure.finite_Lim_measure_decseq
- measure_space.simple_integral_vimage -> simple_integral_distr
- measure_space.integrable_vimage -> integrable_distr
- measure_space.positive_integral_translated_density -> positive_integral_density
- measure_space.integral_translated_density -> integral_density
- measure_space.integral_vimage -> integral_distr
- measure_space_density -> emeasure_density
- measure_space.positive_integral_vimage -> positive_integral_distr
+ measure_space.real_measure_Diff -> measure_Diff
+ measure_space.real_measure_finite_Union -> measure_finite_Union
+ measure_space.real_measure_setsum_singleton -> measure_eq_setsum_singleton
+ measure_space.real_measure_subadditive -> measure_subadditive
+ measure_space.real_measure_Union -> measure_Union
+ measure_space.real_measure_UNION -> measure_UNION
measure_space.simple_function_vimage -> simple_function_comp
measure_space.simple_integral_vimage -> simple_integral_distr
+ measure_space.simple_integral_vimage -> simple_integral_distr
+ measure_unique_Int_stable -> measure_eqI_generator_eq
+ measure_unique_Int_stable_vimage -> measure_eqI_generator_eq
pair_sigma_algebra.measurable_cut_fst -> sets_Pair1
pair_sigma_algebra.measurable_cut_snd -> sets_Pair2
pair_sigma_algebra.measurable_pair_image_fst -> measurable_Pair1
pair_sigma_algebra.measurable_pair_image_snd -> measurable_Pair2
pair_sigma_algebra.measurable_product_swap -> measurable_pair_swap_iff
- pair_sigma_finite.measure_cut_measurable_fst -> pair_sigma_finite.measurable_emeasure_Pair1
- pair_sigma_finite.measure_cut_measurable_snd -> pair_sigma_finite.measurable_emeasure_Pair2
- measure_space.measure_not_negative -> emeasure_not_MInf
- pair_sigma_finite.measure_preserving_swap -> pair_sigma_finite.distr_pair_swap
- pair_sigma_finite.pair_measure_alt -> pair_sigma_finite.emeasure_pair_measure_alt
- pair_sigma_finite.pair_measure_alt2 -> pair_sigma_finite.emeasure_pair_measure_alt2
- pair_sigma_finite.pair_measure_times -> pair_sigma_finite.emeasure_pair_measure_Times
pair_sigma_algebra.pair_sigma_algebra_measurable -> measurable_pair_swap
pair_sigma_algebra.pair_sigma_algebra_swap_measurable -> measurable_pair_swap'
pair_sigma_algebra.sets_swap -> sets_pair_swap
- finite_product_sigma_algebra.in_P -> sets_PiM_I_finite
- Int_stable_product_algebra_generator -> positive_integral
- product_sigma_finite.measure_fold -> product_sigma_finite.distr_merge
- product_sigma_finite.measure_preserving_component_singelton -> product_sigma_finite.distr_singleton
- product_sigma_finite.measure_preserving_merge -> product_sigma_finite.distr_merge
- finite_product_sigma_algebra.P_empty -> space_PiM_empty, sets_PiM_empty
- product_algebra_generator_der -> prod_algebra_eq_finite
- product_algebra_generator_into_space -> prod_algebra_sets_into_space
- product_sigma_algebra.product_algebra_into_space -> space_closed
- product_algebraE -> prod_algebraE_all
- product_algebraI -> sets_PiM_I_finite
- product_measure_exists -> product_sigma_finite.sigma_finite
- sets_product_algebra -> sets_PiM
- sigma_product_algebra_sigma_eq -> sigma_prod_algebra_sigma_eq
- space_product_algebra -> space_PiM
- Int_stable_cuboids -> Int_stable_atLeastAtMost
- measure_space.density_is_absolutely_continuous -> absolutely_continuousI_density
- sigma_finite_measure.RN_deriv_vimage -> sigma_finite_measure.RN_deriv_distr
- prob_space_unique_Int_stable -> measure_eqI_prob_space
- sigma_finite_measure.disjoint_sigma_finite -> sigma_finite_disjoint
+ pair_sigma_finite.measure_cut_measurable_fst -> pair_sigma_finite.measurable_emeasure_Pair1
+ pair_sigma_finite.measure_cut_measurable_snd -> pair_sigma_finite.measurable_emeasure_Pair2
+ pair_sigma_finite.measure_preserving_swap -> pair_sigma_finite.distr_pair_swap
+ pair_sigma_finite.pair_measure_alt2 -> pair_sigma_finite.emeasure_pair_measure_alt2
+ pair_sigma_finite.pair_measure_alt -> pair_sigma_finite.emeasure_pair_measure_alt
+ pair_sigma_finite.pair_measure_times -> pair_sigma_finite.emeasure_pair_measure_Times
+ prob_space.indep_distribution_eq_measure -> prob_space.indep_vars_iff_distr_eq_PiM
+ prob_space.indep_var_distributionD -> prob_space.indep_var_distribution_eq
prob_space.measure_space_1 -> prob_space.emeasure_space_1
prob_space.prob_space_vimage -> prob_space_distr
prob_space.random_variable_restrict -> measurable_restrict
- measure_preserving -> equality "distr M N f = N" "f : measurable M N"
- measure_unique_Int_stable_vimage -> measure_eqI_generator_eq
- measure_space.measure_preserving_Int_stable -> measure_eqI_generator_eq
+ prob_space_unique_Int_stable -> measure_eqI_prob_space
+ product_algebraE -> prod_algebraE_all
+ product_algebra_generator_der -> prod_algebra_eq_finite
+ product_algebra_generator_into_space -> prod_algebra_sets_into_space
+ product_algebraI -> sets_PiM_I_finite
+ product_measure_exists -> product_sigma_finite.sigma_finite
product_prob_space.finite_index_eq_finite_product -> product_prob_space.sets_PiM_generator
product_prob_space.finite_measure_infprod_emb_Pi -> product_prob_space.measure_PiM_emb
- finite_product_prob_space.finite_measure_times -> finite_product_prob_space.finite_measure_PiM_emb
product_prob_space.infprod_spec -> product_prob_space.emeasure_PiM_emb_not_empty
product_prob_space.measurable_component -> measurable_component_singleton
product_prob_space.measurable_emb -> measurable_prod_emb
product_prob_space.measurable_into_infprod_algebra -> measurable_PiM_single
product_prob_space.measurable_singleton_infprod -> measurable_component_singleton
product_prob_space.measure_emb -> emeasure_prod_emb
+ product_prob_space.measure_preserving_restrict -> product_prob_space.distr_restrict
+ product_sigma_algebra.product_algebra_into_space -> space_closed
+ product_sigma_finite.measure_fold -> product_sigma_finite.distr_merge
+ product_sigma_finite.measure_preserving_component_singelton -> product_sigma_finite.distr_singleton
+ product_sigma_finite.measure_preserving_merge -> product_sigma_finite.distr_merge
sequence_space.measure_infprod -> sequence_space.measure_PiM_countable
- product_prob_space.measure_preserving_restrict -> product_prob_space.distr_restrict
- prob_space.indep_distribution_eq_measure -> prob_space.indep_vars_iff_distr_eq_PiM
- prob_space.indep_var_distributionD -> prob_space.indep_var_distribution_eq
- conditional_entropy_positive -> conditional_entropy_nonneg_simple
- conditional_entropy_eq -> conditional_entropy_simple_distributed
- conditional_mutual_information_eq_mutual_information -> conditional_mutual_information_eq_mutual_information_simple
- conditional_mutual_information_generic_positive -> conditional_mutual_information_nonneg_simple
- conditional_mutual_information_positive -> conditional_mutual_information_nonneg_simple
- entropy_commute -> entropy_commute_simple
- entropy_eq -> entropy_simple_distributed
- entropy_generic_eq -> entropy_simple_distributed
- entropy_positive -> entropy_nonneg_simple
- entropy_uniform_max -> entropy_uniform
- KL_eq_0 -> KL_same_eq_0
- KL_eq_0_imp -> KL_eq_0_iff_eq
- KL_ge_0 -> KL_nonneg
- mutual_information_eq -> mutual_information_simple_distributed
- mutual_information_positive -> mutual_information_nonneg_simple
+ sets_product_algebra -> sets_PiM
+ sigma_algebra.measurable_sigma -> measurable_measure_of
+ sigma_finite_measure.disjoint_sigma_finite -> sigma_finite_disjoint
+ sigma_finite_measure.RN_deriv_vimage -> sigma_finite_measure.RN_deriv_distr
+ sigma_product_algebra_sigma_eq -> sigma_prod_algebra_sigma_eq
+ space_product_algebra -> space_PiM
* New "case_product" attribute to generate a case rule doing multiple
case distinctions at the same time. E.g.