Hahn decomposition
From Encyclopedia of Mathematics
Revision as of 18:03, 26 April 2012 by Boris Tsirelson (talk | contribs) (→References: Royden: internal link)
A partition of a set , on which a
-additive set function
is given on the
-algebra
of subsets, into two subsets
and
,
, such that
if
,
, and
if
,
. Such a partition of
is not unique, in general.
References
[1] | N. Dunford, J.T. Schwartz, "Linear operators. General theory" , 1 , Interscience (1958) |
Comments
See also Jordan decomposition. Instead of Hahn decomposition the phrase Hahn–Jordan decomposition is also used.
References
[a1] | P.R. Halmos, "Measure theory" , v. Nostrand (1950) |
[a2] | W. Rudin, "Real and complex analysis" , McGraw-Hill (1966) pp. 57 |
[a3] | H.L. Royden, "Real analysis", Macmillan (1968) |
How to Cite This Entry:
Hahn decomposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hahn_decomposition&oldid=25514
Hahn decomposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hahn_decomposition&oldid=25514
This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article