Regular measure
From Encyclopedia of Mathematics
A measure defined on the Borel -algebra
of a topological space
such that for any Borel set
and any
there is an open set
containing
,
, and such that
. An equivalent definition is as follows: For any
and any
there is a closed set
such that
.
Comments
See also Regular set function.
This notion of regular measure should not be confused with that of a regular outer measure, which is an outer measure (cf. also Measure) such that for every
there is a measurable set
such that
.
References
[a1] | M.E. Munroe, "Introduction to measure and integration" , Addison-Wesley (1953) pp. 111 |
How to Cite This Entry:
Regular measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Regular_measure&oldid=27568
Regular measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Regular_measure&oldid=27568
This article was adapted from an original article by R.A. Minlos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article