Pointwise limit of measures

Asked Jan 25 '13 at 07:28

Active Jan 25 '13 at 07:28

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Limit of measures is again a measure

If $$ P(A) = \lim_n P_n(A)$$ for every $A \in$ $\sigma-$field $\mathcal{F}$. Can we prove that if $P_n$ are probability measures then $P$ is also a probability measure, using Steinhaus's lemma?

edited Apr 13 '17 at 12:20

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asked Jan 25 '13 at 07:28

UnadulteratedImagination

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http://math.stackexchange.com/questions/118592/limit-of-measures-is-again-a-measure – Michael Greinecker Jan 25 '13 at 08:12
And what do you mean by "Steinhaus's lemma"? The only result I know by this name is for a more specialized setting. – Michael Greinecker Jan 25 '13 at 08:18
problem 7 section 1.5 Robert Ash. (http://books.google.co.in/books?id=GkqQoRpCO2QC) – UnadulteratedImagination Jan 25 '13 at 13:03
and yes the above post's answer uses it. – UnadulteratedImagination Jan 25 '13 at 13:05

Pointwise limit of measures

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