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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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: Define
9:= {BC 2:3 countable CB C C such that B E o (CB)}.
Show that G is a o-field that contains C.
Transcribed Image Text: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: Define 9:= {BC 2:3 countable CB C C such that B E o (CB)}. Show that G is a o-field that contains C.
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