src/HOL/Analysis/Nonnegative_Lebesgue_Integration.thy
changeset 69546 27dae626822b
parent 69457 bea49e443909
child 69654 bc758f4f09e5
equal deleted inserted replaced
69545:4aed40ecfb43 69546:27dae626822b
  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)"