Extensions of group-valued set functions |
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Authors: | R Göbel K P S Bhaskara Rao R M Shortt |
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Institution: | 1. Universit?t GHS, Essen, Germany 2. Indian Statistical Institute, Bangalore, India 3. Wesleyan University, Middletown, Connecticut, USA
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Abstract: | The problem of common extension ofcharges (finitely additive measures) is generalised to include group-valued functions defined on a system of sets (u-systems). To eachu-systemU an Abelian groupH(U) is attached. Every Abelian group is isomorphic to one of the formH(U). The groupH(U) is an indicator for extendability of charges fromU to the Boolean algebra generated byU. AllG-valued measures extend if and only if Ext(H(U),G)=0, for instance.
Supported as van Vleck visiting professor at Wesleyan University, Connecticut in 1993.
Partially supported by the Graduierten KollogTheoretische und experimentelle Methoden der reinen Mathematik of Essen University, a project No. G-0294-081.06/93 of the German-Israeli Foundation for Scientific Research & Development
and by the German Academic Exchange, DAAD 1994. |
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Keywords: | Primary 28A99 28A51 20Kxx Secondary 26A45 |
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