Suppose C is a class of subsets of 22 and suppose BC 2 satisfies B € σ (C).Show that there exists a countable class CB C C such that B E O (CB).Hint: Define9:= {BC 2:3 countable CB C C such that B E o (CB)}.Show that G is a o-field that contains C.

Solution: Let 'G' be the union of all σ-algebras generated by countable subsets of CB.

Answered: Suppose C is a class of subsets of $2…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 6E

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Suppose C is a class of subsets of $2 and suppose BC 2 satisfies B € σ (C). Show that there exists a countable class CB C C such that B E O (CB). Hint: Define G:= {BC: 3 countable CB C C such that B € σ (CB)}. Show that G is a o-field that contains C.