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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.

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Unit probability subset of image of a measurable set

Let $(\Omega,\Sigma,P)$ be a probability space and $A\in \Sigma$ be such that $P(A) = 1$. Let $X:\Omega \to \mathbb{R}^n$ be a $\Sigma$-measurable map and $\Lambda_X (B) = P(X \in B)~\forall B \in \ma …
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