src/HOL/Analysis/Sigma_Algebra.thy
changeset 69597 ff784d5a5bfb
parent 69566 c41954ee87cf
child 69661 a03a63b81f44
equal deleted inserted replaced
69596:c8a2755bf220 69597:ff784d5a5bfb
  1635 
  1635 
  1636 lemma space_empty_iff: "space N = {} \<longleftrightarrow> sets N = {{}}"
  1636 lemma space_empty_iff: "space N = {} \<longleftrightarrow> sets N = {{}}"
  1637   by (metis Pow_empty Sup_bot_conv(1) cSup_singleton empty_iff
  1637   by (metis Pow_empty Sup_bot_conv(1) cSup_singleton empty_iff
  1638             sets.sigma_sets_eq sets.space_closed sigma_sets_top subset_singletonD)
  1638             sets.sigma_sets_eq sets.space_closed sigma_sets_top subset_singletonD)
  1639 
  1639 
  1640 subsubsection \<open>Constructing simple @{typ "'a measure"}\<close>
  1640 subsubsection \<open>Constructing simple \<^typ>\<open>'a measure\<close>\<close>
  1641 
  1641 
  1642 proposition emeasure_measure_of:
  1642 proposition emeasure_measure_of:
  1643   assumes M: "M = measure_of \<Omega> A \<mu>"
  1643   assumes M: "M = measure_of \<Omega> A \<mu>"
  1644   assumes ms: "A \<subseteq> Pow \<Omega>" "positive (sets M) \<mu>" "countably_additive (sets M) \<mu>"
  1644   assumes ms: "A \<subseteq> Pow \<Omega>" "positive (sets M) \<mu>" "countably_additive (sets M) \<mu>"
  1645   assumes X: "X \<in> sets M"
  1645   assumes X: "X \<in> sets M"