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On vector lattice-valued measures II

Part of: Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  09 April 2009

T. V. Panchapagesan  and
Shivappa Veerappa Palled
T. V. Panchapagesan
Affiliation:
Departmento de Matematica, Facultad de Ciencias, Universidad de Los Andes, Mrida, Venezuela
Shivappa Veerappa Palled
Affiliation:
Department of Mathematics, State University College at Postdam, Potsdam, New York 13676, U.S.A.
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Abstract

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For a weakly (, )-distributive vector lattice V, it is proved that a V{}-valued Baire measure 0 on a locally compact Hausdorff space T admits uniquely regular Borel and weakly Borel extensions on T if and only if 0 is strongly regular at . Consequently, for such a vector lattice V every V-valued Baire measure on a locally compact Hausdorff space T has unique regular Borel and weakly Borel extensions. Finally some characterisations of a weakly (, )-distributive vector lattice are given in terms of the existence of regular Borel (weakly Borel) extensions of certain V{}-valued Barie measures on locally compact Hausdorff spaces.

MSC classification

Secondary: 28B15: Set functions, measures and integrals with values in ordered spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 2 , April 1986 , pp. 234 - 252
Copyright
Copyright Australian Mathematical Society 1986

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