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Sur les fonctions-vecteurs complètement additives
- Publisher
- de Gruyter
- Copyright
- © by Mona Khare
- ISSN
- 0420-1213
- eISSN
- 2391-4661
- DOI
- 10.1515/dema-2010-0303
- Publisher site
- See Article on Publisher Site
Abstract
DEMONSTRATE MATHEMATICAVol. XLIIINo 32010Mona Khare, Akhilesh Kumar SinghTHE R A N G E OF NON-ATOMIC MEASURES ONEFFECT ALGEBRASAbstract. The present paper deals with the study of superior variation m + , inferiorvariation m~ and total variation |m| of an extended real-valued function m defined onan effect algebra L; having obtained a Jordan type decomposition theorem for a locallybounded real-valued measure m defined on L, we have observed that the range of anon-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, wehave proved an analogue of Lyapunov convexity theorem for this measure.1. IntroductionLet 7i be a Hilbert space and let S(7i) be a partially ordered groupof all bounded self-adjoint operators on 7i. Put E(H) = {A e S(7i) :0 < A < I}. If a quantum mechanical system T is represented in theusual way by a Hilbert space H, then the elements of E(7i) correspondto effects for T [29, 30]. Effects are of significance in representing unsharp measurements or observations on the system T [10], and effect valued measures play an important role in stochastic quantum mechanics
Journal
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 2010