Let A n , n 1, 2, , be independent events in the probability space (, A , P ) Then show that (i) If and only if P (lim sup n A n ) 1 (ii) If and only if P (lim sup n A n ) 0 E P(An) 00...

i Set lim sup m A m m1 im A i Then as m and n That is P c lim m lim n n im PA c i p i PA i ...

Let A n , n = 1, 2,., be independent events in the probability space (, A

Question:

LetA_n,n= 1, 2,€¦., be independent events in the probability space (Î©,A,P). Then show that

(i)

If and only if P(lim sup _n_†’_¥ A_n) = 1.

(ii)

If and only if P(lim sup _n_†’ˆž A_n) = 0.

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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 03:34 AM

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Let A n , n = 1, 2,., be independent events in the probability space (, A

Question:

E P(An) = ∞ 00

Step by Step Answer:

i Set lim sup m A m m1 im A i Then as m and n That is P c lim m lim n n im PA c i p i PA i ...View the full answer

An Introduction to Measure Theoretic Probability

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