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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.

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

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Additional Information

PII: S 0002-9947(1976)0407227-4
Article copyright: © Copyright 1976 American Mathematical Society

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