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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Compactifications of spaces of functions and integration of functionals


Author: L. Š. Grinblat
Journal: Trans. Amer. Math. Soc. 217 (1976), 195-223
MSC: Primary 28A40; Secondary 46E99, 60B10
MathSciNet review: 0407227
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Abstract: For a locally compact space there exists a compactification such that all its points are effectively describable, namely, Alexandroff's onepoint compactification. The effective construction of compactifications for numerous standard separable metric spaces is already a very nontrivial problem. We propose a method of compactification which enables us to effectively construct compactifications of some spaces of functions (for example, of a ball in $ {L_p}( - \infty ,\infty )$). It will be shown that the study of compactifications of spaces of functions is of principal importance in the theory of integration of functionals and in limit theorems for random processes.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0407227-4
PII: S 0002-9947(1976)0407227-4
Article copyright: © Copyright 1976 American Mathematical Society