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| − | ''of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031150/d0311501.png" /> in an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031150/d0311502.png" />-dimensional space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031150/d0311503.png" />''
| + | #REDIRECT[[Density of a set]] |
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| − | A point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031150/d0311504.png" /> at which the density of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031150/d0311505.png" /> (cf. [[Density of a set|Density of a set]]) is equal to one. If the outer density is equal to one, the point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031150/d0311506.png" /> 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|approximate continuity]] and of an [[Approximate derivative|approximate derivative]] of a function.
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| − | ====Comments====
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| − | For references see [[Density of a set|Density of a set]].
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Revision as of 15:25, 5 August 2012
How to Cite This Entry:
Density point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Density_point&oldid=14977
This article was adapted from an original article by V.A. Skvortsov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article