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m Typo fixing, etc., typo(s) fixed: Moreover → Moreover, using AWB |
→Alternate definition: 'U' is not a neighborhood of 't', it is a subset of the abstract probability space. |
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where the [[Limit (mathematics)|limit]] is taken over the [[Net (mathematics)|net]] of [[Open set|open]] [[Neighbourhood (mathematics)|neighborhoods]] ''U'' of ''t'' as they become [[Subset|smaller with respect to set inclusion]]. This limit is defined if and only if the probability space is [[Radon space|Radon]], and only in the support of ''T'', as described in the article. This is the restriction of the transition probability to the support of ''T''. To describe this limiting process rigorously:
For every <math>\epsilon > 0,</math> there exists an open neighborhood ''U'' of the event {''T=t''}, such that for every open ''V'' with <math>\{T=t\} \
:<math>\left|\frac {P(A\cap V)}{P(V)}-L\right| < \epsilon,</math>
where <math>L = P (A|T=t)</math> is the limit.
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