src/HOL/Analysis/Binary_Product_Measure.thy
changeset 67399 eab6ce8368fa
parent 64267 b9a1486e79be
child 67693 4fa9d5ef95bc
equal deleted inserted replaced
67398:5eb932e604a2 67399:eab6ce8368fa
   161   "f \<in> measurable M (M1 \<Otimes>\<^sub>M M2) \<longleftrightarrow> (fst \<circ> f) \<in> measurable M M1 \<and> (snd \<circ> f) \<in> measurable M M2"
   161   "f \<in> measurable M (M1 \<Otimes>\<^sub>M M2) \<longleftrightarrow> (fst \<circ> f) \<in> measurable M M1 \<and> (snd \<circ> f) \<in> measurable M M2"
   162   by (auto intro: measurable_pair[of f M M1 M2])
   162   by (auto intro: measurable_pair[of f M M1 M2])
   163 
   163 
   164 lemma measurable_split_conv:
   164 lemma measurable_split_conv:
   165   "(\<lambda>(x, y). f x y) \<in> measurable A B \<longleftrightarrow> (\<lambda>x. f (fst x) (snd x)) \<in> measurable A B"
   165   "(\<lambda>(x, y). f x y) \<in> measurable A B \<longleftrightarrow> (\<lambda>x. f (fst x) (snd x)) \<in> measurable A B"
   166   by (intro arg_cong2[where f="op \<in>"]) auto
   166   by (intro arg_cong2[where f="(\<in>)"]) auto
   167 
   167 
   168 lemma measurable_pair_swap': "(\<lambda>(x,y). (y, x)) \<in> measurable (M1 \<Otimes>\<^sub>M M2) (M2 \<Otimes>\<^sub>M M1)"
   168 lemma measurable_pair_swap': "(\<lambda>(x,y). (y, x)) \<in> measurable (M1 \<Otimes>\<^sub>M M2) (M2 \<Otimes>\<^sub>M M1)"
   169   by (auto intro!: measurable_Pair simp: measurable_split_conv)
   169   by (auto intro!: measurable_Pair simp: measurable_split_conv)
   170 
   170 
   171 lemma measurable_pair_swap:
   171 lemma measurable_pair_swap: