= Random element
{title2=$X:\Omega\to E$}
A random element is a <measurable function> from a <probability space> $(\Omega,\mathcal F,\mathbb P)$ to a <measurable space> $(E,\mathcal E)$. Its law is the <pushforward measure> $\mathbb P_X(A)=\mathbb P(X^{-1}(A))$ for $A\in\mathcal E$. Real-valued <random variables> and vector-valued random variables are examples; a stochastic sample path can also be a random element when its path-space sigma-algebra is specified. For a <Polish space> $E$, the usual choice is its <Borel sigma-algebra>. A <large deviation principle> concerns the laws of a family of such random elements.
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