src/HOL/Probability/Levy.thy
changeset 64283 979cdfdf7a79
parent 63886 685fb01256af
child 64284 f3b905b2eee2
equal deleted inserted replaced
64282:261d42f0bfac 64283:979cdfdf7a79
   388       by (intro integrableI_bounded_set_indicator[where B=2]) (auto simp: emeasure_lborel_Icc_eq)
   388       by (intro integrableI_bounded_set_indicator[where B=2]) (auto simp: emeasure_lborel_Icc_eq)
   389     have 3: "\<And>u v. set_integrable lborel {u..v} (\<lambda>x. cmod (1 - char M' x))"
   389     have 3: "\<And>u v. set_integrable lborel {u..v} (\<lambda>x. cmod (1 - char M' x))"
   390       by (intro borel_integrable_compact[OF compact_Icc] continuous_at_imp_continuous_on
   390       by (intro borel_integrable_compact[OF compact_Icc] continuous_at_imp_continuous_on
   391                 continuous_intros ballI M'.isCont_char continuous_intros)
   391                 continuous_intros ballI M'.isCont_char continuous_intros)
   392     have "cmod (CLBINT t:{-d/2..d/2}. 1 - char M' t) \<le> LBINT t:{-d/2..d/2}. cmod (1 - char M' t)"
   392     have "cmod (CLBINT t:{-d/2..d/2}. 1 - char M' t) \<le> LBINT t:{-d/2..d/2}. cmod (1 - char M' t)"
   393       using integral_norm_bound[OF 2] by simp
   393       using integral_norm_bound[of _ "\<lambda>x. indicator {u..v} x *\<^sub>R (1 - char M' x)" for u v] by simp
   394     also have 4: "\<dots> \<le> LBINT t:{-d/2..d/2}. \<epsilon> / 4"
   394     also have 4: "\<dots> \<le> LBINT t:{-d/2..d/2}. \<epsilon> / 4"
   395       apply (rule integral_mono [OF 3])
   395       apply (rule integral_mono [OF 3])
   396        apply (simp add: emeasure_lborel_Icc_eq)
   396        apply (simp add: emeasure_lborel_Icc_eq)
   397       apply (case_tac "x \<in> {-d/2..d/2}")
   397       apply (case_tac "x \<in> {-d/2..d/2}")
   398        apply auto
   398        apply auto