equal
deleted
inserted
replaced
806 (insert assms, auto simp: scaleR_sum_left) |
806 (insert assms, auto simp: scaleR_sum_left) |
807 qed |
807 qed |
808 finally show ?thesis . |
808 finally show ?thesis . |
809 qed |
809 qed |
810 |
810 |
811 lemma continuous_on_LINT_pmf: -- \<open>This is dominated convergence!?\<close> |
811 lemma continuous_on_LINT_pmf: \<comment> \<open>This is dominated convergence!?\<close> |
812 fixes f :: "'i \<Rightarrow> 'a::topological_space \<Rightarrow> 'b::{banach, second_countable_topology}" |
812 fixes f :: "'i \<Rightarrow> 'a::topological_space \<Rightarrow> 'b::{banach, second_countable_topology}" |
813 assumes f: "\<And>i. i \<in> set_pmf M \<Longrightarrow> continuous_on A (f i)" |
813 assumes f: "\<And>i. i \<in> set_pmf M \<Longrightarrow> continuous_on A (f i)" |
814 and bnd: "\<And>a i. a \<in> A \<Longrightarrow> i \<in> set_pmf M \<Longrightarrow> norm (f i a) \<le> B" |
814 and bnd: "\<And>a i. a \<in> A \<Longrightarrow> i \<in> set_pmf M \<Longrightarrow> norm (f i a) \<le> B" |
815 shows "continuous_on A (\<lambda>a. LINT i|M. f i a)" |
815 shows "continuous_on A (\<lambda>a. LINT i|M. f i a)" |
816 proof cases |
816 proof cases |