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Hahn decomposition

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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
This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article