Hahn decomposition

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)