Limit of distributions

In mathematics, specifically in the theory of generalized functions, the limit of a sequence of distributions is the distribution that sequence approaches. The distance, suitably quantified, to the limiting distribution can be made arbitrarily small by selecting a distribution sufficiently far along the sequence. This notion generalizes a limit of a sequence of functions; a limit as a distribution may exist when a limit of functions does not.

This article is about limits of sequences of generalized functions. For limits of probability distributions, see Convergence of random variables ยง Convergence in distribution.

The notion is a part of distributional calculus, a generalized form of calculus that is based on the notion of distributions, as opposed to classical calculus, which is based on the narrower concept of functions.

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