The range of non-atomic measures on effect algebras

• Autorzy: Khare M. , Singh A. K.
• Języki publikacji: EN

Abstrakty

EN

The present paper deals with the study of superior variation m+, inferior variation m¯ and total variation |m| of an extended real-valued function m defined on an effect algebra L; having obtained a Jordan type decomposition theorem for a locally bounded real-valued measure m defined on L, we have observed that the range of a non-atomic function m defined on a D-lattice L is an interval (—m¯ (1), m+(1)). Finally, after introducing the notion of a relatively non-atomic measure on an effect algebra L, we have proved an analogue of Lyapunov convexity theorem for this measure.

Słowa kluczowe

EN

effect algebra; superior variation; inferior variation; total variation; Jordan type decomposition theorem; m-atoms; non-atomic measure; relative non-atomic measure; convexity theorem

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 3
• Strony: 497--510
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Khare M.

autor

Singh A. K.

• Department of Mathematics University of Allahabad Allahabad-211002, India Mailing address: 10 C.S.P. Singh Marg Allahabad-211 001, India,

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