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Let K be the collection of all compact sets in R and Cx the collection of all countable subsets of K. For the Borel o-algebra on R, prove that B(R)= Uo(C), CECK where o(C) denotes the smallest o-algebra on R containing C.

Let K be the collection of all compact sets in R and Cx the collection of all countable subsets of K. For the Borel o-algebra on R, prove that B(R)= Uo(C), CECK where o(C) denotes the smallest o-algebra on R containing C.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...
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Hint is to show that B(ℝ) is the smallest σ-algebra on ℝ containing K.

Let K be the collection of all compact sets in R and Cx the collection of all countable subsets of K. For the Borel o-algebra on R, prove that B(R) = o(C), CECK where σ (C) denotes the smallest o-algebra on R containing C.
Transcribed Image Text:Let K be the collection of all compact sets in R and Cx the collection of all countable subsets of K. For the Borel o-algebra on R, prove that B(R) = o(C), CECK where σ (C) denotes the smallest o-algebra on R containing C.
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