src/HOL/Analysis/Bochner_Integration.thy
changeset 69546 27dae626822b
parent 69144 f13b82281715
child 69566 c41954ee87cf
equal deleted inserted replaced
69545:4aed40ecfb43 69546:27dae626822b
   522 
   522 
   523 lemma%unimportant has_bochner_integral_cong:
   523 lemma%unimportant has_bochner_integral_cong:
   524   assumes "M = N" "\<And>x. x \<in> space N \<Longrightarrow> f x = g x" "x = y"
   524   assumes "M = N" "\<And>x. x \<in> space N \<Longrightarrow> f x = g x" "x = y"
   525   shows "has_bochner_integral M f x \<longleftrightarrow> has_bochner_integral N g y"
   525   shows "has_bochner_integral M f x \<longleftrightarrow> has_bochner_integral N g y"
   526   unfolding has_bochner_integral.simps assms(1,3)
   526   unfolding has_bochner_integral.simps assms(1,3)
   527   using assms(2) by (simp cong: measurable_cong_strong nn_integral_cong_strong)
   527   using assms(2) by (simp cong: measurable_cong_simp nn_integral_cong_simp)
   528 
   528 
   529 lemma%unimportant has_bochner_integral_cong_AE:
   529 lemma%unimportant has_bochner_integral_cong_AE:
   530   "f \<in> borel_measurable M \<Longrightarrow> g \<in> borel_measurable M \<Longrightarrow> (AE x in M. f x = g x) \<Longrightarrow>
   530   "f \<in> borel_measurable M \<Longrightarrow> g \<in> borel_measurable M \<Longrightarrow> (AE x in M. f x = g x) \<Longrightarrow>
   531     has_bochner_integral M f x \<longleftrightarrow> has_bochner_integral M g x"
   531     has_bochner_integral M f x \<longleftrightarrow> has_bochner_integral M g x"
   532   unfolding has_bochner_integral.simps
   532   unfolding has_bochner_integral.simps