Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] J. L. Kelley and T. P. Srinivasan, Pre-measures on lattices of sets, Math. Ann. 190 (1970/71), 233-241. MR 43 #4990. MR 0279267 (43:4990)
  • [2] J. L. Kelley, M. K. Nayak and T. P. Srinivasan, Pre-measures on lattices of sets. II, Sympos. on Vector Measures, Salt Lake City, Utah, 1972. MR 0333108 (48:11433)
  • [3] I. Kluvanek, Vector and operator valued measures and applications, (Proc. Sympos., Snowbird Resort, Alta, Utah, 1972), Academic Press, New York, 1973, p. 178. MR 0335741 (49:521)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A45

Retrieve articles in all journals with MSC: 28A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0369653-6
Keywords: Tight, modular, continuous at $ \emptyset $.
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society