Density point

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of a set in an -dimensional space

A point at which the density of (cf. Density of a set) is equal to one. If the outer density is equal to one, the point is called an outer density point. A density point of a set is simultaneously a point of thinness for the complement of this set. Almost-all points in a measurable set are density points of it. By means of the concept of a density point one may introduce the concepts of approximate continuity and of an approximate derivative of a function.


For references see Density of a set.

How to Cite This Entry:
Density point. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.A. Skvortsov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article