Difference between revisions of "Hahn decomposition"
From Encyclopedia of Mathematics
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| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> P.R. Halmos, "Measure theory" , v. Nostrand (1950)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> W. Rudin, "Real and complex analysis" , McGraw-Hill (1966) pp. 57</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> H.L. Royden, | + | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> P.R. Halmos, "Measure theory" , v. Nostrand (1950)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> W. Rudin, "Real and complex analysis" , McGraw-Hill (1966) pp. 57</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> H.L. Royden, [[Royden, "Real analysis"|"Real analysis"]], Macmillan (1968)</TD></TR></table> |
Revision as of 18:03, 26 April 2012
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=13726
Hahn decomposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hahn_decomposition&oldid=13726
This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article