equal
deleted
inserted
replaced
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) |