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A new proof of the Sobczyk-Hammer decomposition theorem. (English) Zbl 1276.28005

The author gives a simple proof of the Sobczyk-Hammer decomposition theorem in terms of Dedekind complete Riesz spaces. (See [A. Sobczyk and P. C. Hammer, Duke Math. J. 11, 839–846 (1944; Zbl 0063.07111)].)

MSC:

28A10 Real- or complex-valued set functions
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces

Citations:

Zbl 0063.07111
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References:

[1] C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis. A Hitchhiker’s Guide , Springer, Berlin, 2006. · Zbl 1156.46001
[2] G. Barbieri, A. Valente and H. Weber, Decomposition of l-group valued measures , Czechoslovak Math. Journal, · Zbl 1274.28025
[3] W. Siebe, On the Sobczyk-Hammer decomposition of additive set functions , Proc. Amer. Math. Soc. 86 (3) (1982) 447-450. · Zbl 0506.28002
[4] A. Sobczyk and P. C. Hammer, A decomposition of additive set functions , Duke Math. J. 11 (1944) 839-846. · Zbl 0063.07111
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