equal
deleted
inserted
replaced
2056 using s by (auto simp: image_subset_iff) |
2056 using s by (auto simp: image_subset_iff) |
2057 from s show "s \<le> f" |
2057 from s show "s \<le> f" |
2058 by (subst s_eq) (auto simp: image_subset_iff le_fun_def split: split_indicator split_indicator_asm) |
2058 by (subst s_eq) (auto simp: image_subset_iff le_fun_def split: split_indicator split_indicator_asm) |
2059 qed |
2059 qed |
2060 then show ?thesis |
2060 then show ?thesis |
2061 unfolding nn_integral_def_finite by (simp cong del: SUP_cong_strong) |
2061 unfolding nn_integral_def_finite by (simp cong del: SUP_cong_simp) |
2062 qed |
2062 qed |
2063 |
2063 |
2064 lemma nn_integral_count_space_indicator: |
2064 lemma nn_integral_count_space_indicator: |
2065 assumes "NO_MATCH (UNIV::'a set) (X::'a set)" |
2065 assumes "NO_MATCH (UNIV::'a set) (X::'a set)" |
2066 shows "(\<integral>\<^sup>+x. f x \<partial>count_space X) = (\<integral>\<^sup>+x. f x * indicator X x \<partial>count_space UNIV)" |
2066 shows "(\<integral>\<^sup>+x. f x \<partial>count_space X) = (\<integral>\<^sup>+x. f x * indicator X x \<partial>count_space UNIV)" |