See also [[Conditional expectation#Definition of conditional probability|conditional probability]] and [[Conditional probability distribution#Measure-Theoretic Formulation|conditional probability distribution]].
==Alternate definition==
{{disputeabout|'''this way leads to irregular conditional probability'''|Non-regular conditional probability|date=September 2009}}
Consider a Radon space <math> \Omega </math> (that is a probability measure defined on a Radon space endowed with the Borel sigma-algebra) and a real-valued random variable ''T''. As discussed above, in this case there exists a regular conditional probability with respect to ''T''. Moreover, we can alternatively define the '''regular conditional probability''' for an event ''A'' given a particular value ''t'' of the random variable ''T'' in the following manner:
:<math> P (A|T=t) = \lim_{U\supset \{T= t\}} \frac {P(A\cap U)}{P(U)},</math>
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\} \subset V \subset U,</math>
