Compactifications of spaces of functions and integration of functionals
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- by L. Š. Grinblat PDF
- Trans. Amer. Math. Soc. 217 (1976), 195-223 Request permission
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
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 217 (1976), 195-223
- MSC: Primary 28A40; Secondary 46E99, 60B10
- DOI: https://doi.org/10.1090/S0002-9947-1976-0407227-4
- MathSciNet review: 0407227