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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Scalar and vector valued premeasures


Authors: M. K. Nayak and T. P. Srinivasan
Journal: Proc. Amer. Math. Soc. 48 (1975), 391-396
MSC: Primary 28A45
DOI: https://doi.org/10.1090/S0002-9939-1975-0369653-6
MathSciNet review: 0369653
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Abstract: A real valued (respectively Banach space valued) set-function on a lattice of sets extends to a $\sigma$-additive measure on a $\sigma$-field provided it is finitely additive tight, continuous at $\emptyset$ and has a bounded (respectively conditionally weakly compact) range.


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Keywords: Tight, modular, continuous at <IMG WIDTH="16" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\emptyset$">.
Article copyright: © Copyright 1975 American Mathematical Society