TY - JOUR

T1 - Compactifications of spaces of functions and integration of functionals

AU - Grinblat, L.

PY - 1976

Y1 - 1976

N2 - For a locally compact space there exists a compactification such that all its points are effectively describable, namely, Alexandroffs one- point 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 Lp(— ∞, ∞)). 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.

AB - For a locally compact space there exists a compactification such that all its points are effectively describable, namely, Alexandroffs one- point 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 Lp(— ∞, ∞)). 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.

UR - http://www.scopus.com/inward/record.url?scp=0039309296&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1976-0407227-4

DO - 10.1090/S0002-9947-1976-0407227-4

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AN - SCOPUS:0039309296

SN - 0002-9947

VL - 217

SP - 195

EP - 223

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -