src/HOL/Probability/Nonnegative_Lebesgue_Integration.thy
changeset 59779 b6bda9140e39
parent 59587 8ea7b22525cb
child 60064 63124d48a2ee
equal deleted inserted replaced
59778:fe5b796d6b2a 59779:b6bda9140e39
  1953   then show ?thesis
  1953   then show ?thesis
  1954     unfolding nn_integral_def_finite SUP_def by simp
  1954     unfolding nn_integral_def_finite SUP_def by simp
  1955 qed
  1955 qed
  1956 
  1956 
  1957 lemma nn_integral_count_space_indicator:
  1957 lemma nn_integral_count_space_indicator:
  1958   assumes "NO_MATCH (X::'a set) (UNIV::'a set)"
  1958   assumes "NO_MATCH (UNIV::'a set) (X::'a set)"
  1959   shows "(\<integral>\<^sup>+x. f x \<partial>count_space X) = (\<integral>\<^sup>+x. f x * indicator X x \<partial>count_space UNIV)"
  1959   shows "(\<integral>\<^sup>+x. f x \<partial>count_space X) = (\<integral>\<^sup>+x. f x * indicator X x \<partial>count_space UNIV)"
  1960   by (simp add: nn_integral_restrict_space[symmetric] restrict_count_space)
  1960   by (simp add: nn_integral_restrict_space[symmetric] restrict_count_space)
  1961 
  1961 
  1962 lemma nn_integral_count_space_eq:
  1962 lemma nn_integral_count_space_eq:
  1963   "(\<And>x. x \<in> A - B \<Longrightarrow> f x = 0) \<Longrightarrow> (\<And>x. x \<in> B - A \<Longrightarrow> f x = 0) \<Longrightarrow>
  1963   "(\<And>x. x \<in> A - B \<Longrightarrow> f x = 0) \<Longrightarrow> (\<And>x. x \<in> B - A \<Longrightarrow> f x = 0) \<Longrightarrow>