2.6. Let (N, F, P) be a probability space and let A1, A2,... be sets in F such that EP(Ak) < ∞ . k=1 Prove the Borel-Cantelli lemma: P(N U Ak) = 0, m=1 k=m i.e. the probability that w belongs to infinitely many As is zero.
2.6. Let (N, F, P) be a probability space and let A1, A2,... be sets in F such that EP(Ak) < ∞ . k=1 Prove the Borel-Cantelli lemma: P(N U Ak) = 0, m=1 k=m i.e. the probability that w belongs to infinitely many As is zero.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:2.6. Let (2, F, P) be a probability space and let A1, A2,... be sets in F
such that
P(Ag) < ∞ .
k=1
Prove the Borel-Cantelli lemma:
P(N U Ak) = 0,
m=1 k=m
i.e. the probability that w belongs to infinitely many A{s is zero.
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