Difference between revisions of "Baire set"
From Encyclopedia of Mathematics
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| − | ''in a locally compact Hausdorff space | + | {{TEX|done}} |
| + | ''in a locally compact Hausdorff space $X$'' | ||
{{MSC|28A05|03E15,54H05}} | {{MSC|28A05|03E15,54H05}} | ||
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[[Category:Classical measure theory]] | [[Category:Classical measure theory]] | ||
| − | A set belonging to the | + | A set belonging to the $\sigma$-ring generated by the class of all compact sets in $X$ that are $G_\delta$-sets. A Baire set serves to define the concept of a Baire-measurable function. In all classical particular cases in which measure theory is developed in topological spaces, e.g. in Euclidean spaces, the concept of a Baire set coincides with that of a [[Borel set|Borel set]]. |
====References==== | ====References==== | ||
| − | + | {| | |
| + | |valign="top"|{{Ref|H}}|| P.R. Halmos, "Measure theory" , v. Nostrand (1950) {{MR|0033869}} {{ZBL|0040.16802}} | ||
| + | |} | ||
Latest revision as of 15:04, 1 May 2014
in a locally compact Hausdorff space $X$
2020 Mathematics Subject Classification: Primary: 28A05 Secondary: 03E1554H05 [MSN][ZBL]
A set belonging to the $\sigma$-ring generated by the class of all compact sets in $X$ that are $G_\delta$-sets. A Baire set serves to define the concept of a Baire-measurable function. In all classical particular cases in which measure theory is developed in topological spaces, e.g. in Euclidean spaces, the concept of a Baire set coincides with that of a Borel set.
References
| [H] | P.R. Halmos, "Measure theory" , v. Nostrand (1950) MR0033869 Zbl 0040.16802 |
How to Cite This Entry:
Baire set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Baire_set&oldid=20663
Baire set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Baire_set&oldid=20663
This article was adapted from an original article by V.A. Skvortsov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article