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Union of increasing sigma-algebras is not sigma-algebra
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[QUOTE="Stephen Tashi, post: 4991158, member: 186655"] Unless the subset relation has a specialized meaning for sigma algebras, I think you are free to use different "whole spaces" for the different sigma algebras, as long as the "whole space" set for [itex] \mathscr A_i [/itex] is a subset of the sets in [itex] \mathscr A_{i+1} [/itex]. Pick a sequence of sigma algebras with finite "whole"spaces" You can form an infinite set by taking a countable union of sets from the finite sets. [/QUOTE]
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Union of increasing sigma-algebras is not sigma-algebra
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