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Baire and |
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| Authors: | T V Panchapagesan |
| Institution: | Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida, Venezuela |
| Abstract: | Let  be a locally compact Hausdorff space and let  be the Banach space of all bounded complex Radon measures on  . Let  and  be the  -rings generated by the compact  subsets and by the compact subsets of  , respectively. The members of  are called Baire sets of  and those of  are called  -Borel sets of  (since they are precisely the  -bounded Borel sets of  ). Identifying  with the Banach space of all Borel regular complex measures on  , in this note we characterize weakly compact subsets  of  in terms of the Baire and  -Borel restrictions of the members of  . These characterizations permit us to give a generalization of a theorem of Dieudonné which is stronger and more natural than that given by Grothendieck. |
| Keywords: | Bounded complex Radon measures uniform $\sigma$-additivity uniform Baire inner regularity uniform $\sigma$-Borel inner regularity uniform Borel inner regularity weakly compact sets |
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