src/HOL/Analysis/Infinite_Set_Sum.thy
changeset 70136 f03a01a18c6e
parent 69710 61372780515b
child 71633 07bec530f02e
equal deleted inserted replaced
70135:ad6d4a14adb5 70136:f03a01a18c6e
    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)