src/HOL/Probability/Probability_Mass_Function.thy
changeset 67226 ec32cdaab97b
parent 66804 3f9bb52082c4
child 67399 eab6ce8368fa
equal deleted inserted replaced
67225:cb34f5f49a08 67226:ec32cdaab97b
   806          (insert assms, auto simp: scaleR_sum_left)
   806          (insert assms, auto simp: scaleR_sum_left)
   807   qed
   807   qed
   808   finally show ?thesis .
   808   finally show ?thesis .
   809 qed
   809 qed
   810 
   810 
   811 lemma continuous_on_LINT_pmf: -- \<open>This is dominated convergence!?\<close>
   811 lemma continuous_on_LINT_pmf: \<comment> \<open>This is dominated convergence!?\<close>
   812   fixes f :: "'i \<Rightarrow> 'a::topological_space \<Rightarrow> 'b::{banach, second_countable_topology}"
   812   fixes f :: "'i \<Rightarrow> 'a::topological_space \<Rightarrow> 'b::{banach, second_countable_topology}"
   813   assumes f: "\<And>i. i \<in> set_pmf M \<Longrightarrow> continuous_on A (f i)"
   813   assumes f: "\<And>i. i \<in> set_pmf M \<Longrightarrow> continuous_on A (f i)"
   814     and bnd: "\<And>a i. a \<in> A \<Longrightarrow> i \<in> set_pmf M \<Longrightarrow> norm (f i a) \<le> B"
   814     and bnd: "\<And>a i. a \<in> A \<Longrightarrow> i \<in> set_pmf M \<Longrightarrow> norm (f i a) \<le> B"
   815   shows "continuous_on A (\<lambda>a. LINT i|M. f i a)"
   815   shows "continuous_on A (\<lambda>a. LINT i|M. f i a)"
   816 proof cases
   816 proof cases