E =U E, E; E;= 0, i ± j. Ej, %3D

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Theorem 6.9 (Countable additivity of the integral). Let E be
union of a finite or a countable family of pairwise disjoint measurable sets
i.e.
E =U E;, E;n E;= 0, i ± j.
Then for any non-negative measurable function f defined on the set E
SAx)dx = E fx)dx.
i E
%3D
Transcribed Image Text:Theorem 6.9 (Countable additivity of the integral). Let E be union of a finite or a countable family of pairwise disjoint measurable sets i.e. E =U E;, E;n E;= 0, i ± j. Then for any non-negative measurable function f defined on the set E SAx)dx = E fx)dx. i E %3D
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