Discontinuous function
From Encyclopedia of Mathematics
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.
Examples.
 | (1) |
 | (2) |
How to Cite This Entry:
Discontinuous function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discontinuous_function&oldid=11471
Discontinuous function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discontinuous_function&oldid=11471
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article