Perron integral

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A generalization of the concept of the Lebesgue integral. A function is said to be integrable in the sense of Perron over if there exist functions (a major function) and (a minor function) such that  ( and are the upper and lower derivatives) for , and if the lower bound to the values of the majorants is equal to the upper bound of the values of the minorants . Their common value is called the Perron integral of over and is denoted by The Perron integral recovers a function from its pointwise finite derivative; it is equivalent to the narrow Denjoy integral. The Perron integral for bounded functions was introduced by O. Perron , while the final definition was given by H. Bauer .

How to Cite This Entry:
Perron integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Perron_integral&oldid=11984
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article