src/HOL/Probability/Giry_Monad.thy
changeset 59978 c2dc7856e2e5
parent 59778 fe5b796d6b2a
child 60067 f1a5bcf5658f
equal deleted inserted replaced
59977:ad2d1cd53877 59978:c2dc7856e2e5
   322   also have "?f \<in> ?M \<longleftrightarrow> (\<lambda>a. emeasure a (space a)) \<in> ?M"
   322   also have "?f \<in> ?M \<longleftrightarrow> (\<lambda>a. emeasure a (space a)) \<in> ?M"
   323     by (rule measurable_cong) (auto simp: space_subprob_algebra dest: sets_eq_imp_space_eq)
   323     by (rule measurable_cong) (auto simp: space_subprob_algebra dest: sets_eq_imp_space_eq)
   324   finally show ?thesis .
   324   finally show ?thesis .
   325 qed
   325 qed
   326 
   326 
   327 (* TODO: Rename. This name is too general – Manuel *)
   327 (* TODO: Rename. This name is too general -- Manuel *)
   328 lemma measurable_pair_measure:
   328 lemma measurable_pair_measure:
   329   assumes f: "f \<in> measurable M (subprob_algebra N)"
   329   assumes f: "f \<in> measurable M (subprob_algebra N)"
   330   assumes g: "g \<in> measurable M (subprob_algebra L)"
   330   assumes g: "g \<in> measurable M (subprob_algebra L)"
   331   shows "(\<lambda>x. f x \<Otimes>\<^sub>M g x) \<in> measurable M (subprob_algebra (N \<Otimes>\<^sub>M L))"
   331   shows "(\<lambda>x. f x \<Otimes>\<^sub>M g x) \<in> measurable M (subprob_algebra (N \<Otimes>\<^sub>M L))"
   332 proof (rule measurable_subprob_algebra)
   332 proof (rule measurable_subprob_algebra)