equal
deleted
inserted
replaced
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" |