Finite-dimensional distribution

In mathematics, finite-dimensional distributions are a tool in the study of measures and . A lot of information can be gained by studying the "projection" of a measure (or process) onto a finite-dimensional vector space (or finite collection of times).

Let ${\displaystyle (X,{\mathcal {F}},\mu )}$ be a measure space. The finite-dimensional distributions of ${\displaystyle \mu }$ are the pushforward measures ${\displaystyle f_{*}(\mu )}$, where ${\displaystyle f:X\to \mathbb {R} ^{k}}$, ${\displaystyle k\in \mathbb {N} }$, is any measurable function.

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