Show that, if An , n 1, is a non decreasing sequence of fields, then n 1 An is always a field, but it may fail to be a fields ...

Set F n 1 A n and let A F Then A A n for some n so that ...

Show that, if {An}, n 1, is a non-decreasing sequence of -fields, then n = 1

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Show that, if {An}, n ≥ 1, is a non-decreasing sequence of σ-fields, then ∪∞n = 1 An is always a field, but it may fail to be a σ-fields.

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An Introduction to Measure Theoretic Probability

ISBN: 978-0128000427

2nd edition

Authors: George G. Roussas

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Question Posted: Mar 25, 2016 03:16 AM

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Show that, if {An}, n 1, is a non-decreasing sequence of -fields, then n = 1

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An Introduction to Measure Theoretic Probability

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