Discontinuous function

From Encyclopedia of Mathematics
Revision as of 16:55, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A function , where and are topological spaces, that is not a continuous function on . The Baire classes, the piecewise-continuous functions and the step functions are important classes of discontinuous real-valued functions .

Discontinuous functions occur, for example, when integrating elementary functions with respect to a parameter (see Dirichlet discontinuous multiplier), when calculating the sum of a series in which the terms are elementary functions, in particular when calculating the sum of a trigonometric series, and in optimal control problems.


How to Cite This Entry:
Discontinuous function. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article