Measures in Denumerable Spaces

Hanisch, Herman; Hirsch, Warren M.; Rényi, A.

doi:10.1080/00029890.1969.12000246

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Main Results From the Techniques Of Douglas1

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1976

1991

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Cited by 4 publications

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“…1. Theorem 2 holds in the case ca(2,»», 2') = {it} if it is possible to extend probability measures on a-fields 2" (2 C 2" C 2') to 2', for example if S is countable (see [5]). But even in the case where 5 is compact and 2, resp.…”

Section: Main Results From the Techniques Of Douglasmentioning

confidence: 99%

Extremal and monogenic additive set functions

Plachky¹

1976

Proc. Amer. Math. Soc.

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Abstract.The extreme points of the convex set of all additive set functions on a field, which coincide on a subfield are characterized by a simple approximation property. It is proved that a stronger approximation property is characteristic for a so-called monogenic additive set function on a field, which can be generated uniquely by an additive set function on a subfield. Finally it is shown that a simple decomposition property must hold if the convex set above has a finite number of extreme points.

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Section: Main Results From the Techniques Of Douglasmentioning

confidence: 99%