equal
deleted
inserted
replaced
72 emeasure (count_space (Pi\<^sub>E A B)) {f}" . |
72 emeasure (count_space (Pi\<^sub>E A B)) {f}" . |
73 qed (simp_all add: countable_PiE assms) |
73 qed (simp_all add: countable_PiE assms) |
74 |
74 |
75 |
75 |
76 |
76 |
77 definition%important abs_summable_on :: |
77 definition\<^marker>\<open>tag important\<close> abs_summable_on :: |
78 "('a \<Rightarrow> 'b :: {banach, second_countable_topology}) \<Rightarrow> 'a set \<Rightarrow> bool" |
78 "('a \<Rightarrow> 'b :: {banach, second_countable_topology}) \<Rightarrow> 'a set \<Rightarrow> bool" |
79 (infix "abs'_summable'_on" 50) |
79 (infix "abs'_summable'_on" 50) |
80 where |
80 where |
81 "f abs_summable_on A \<longleftrightarrow> integrable (count_space A) f" |
81 "f abs_summable_on A \<longleftrightarrow> integrable (count_space A) f" |
82 |
82 |
83 |
83 |
84 definition%important infsetsum :: |
84 definition\<^marker>\<open>tag important\<close> infsetsum :: |
85 "('a \<Rightarrow> 'b :: {banach, second_countable_topology}) \<Rightarrow> 'a set \<Rightarrow> 'b" |
85 "('a \<Rightarrow> 'b :: {banach, second_countable_topology}) \<Rightarrow> 'a set \<Rightarrow> 'b" |
86 where |
86 where |
87 "infsetsum f A = lebesgue_integral (count_space A) f" |
87 "infsetsum f A = lebesgue_integral (count_space A) f" |
88 |
88 |
89 syntax (ASCII) |
89 syntax (ASCII) |