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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

8 votes
4 answers
2k views

Is every probability measure a pushforward of Lebesgue measure?

If $m$ is a probability measure on a measurable space $(X, \Sigma)$, is there necessarily a measurable function $f : [0, 1] \to X$ such that $m(A) = \mu(f^{-1}(A))$ for all $A \in \Sigma$? ($\mu$ is …
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