Weak-star convergence in the dual of the continuous functions on the -cube,

Authors:
Richard B. Darst and Zorabi Honargohar

Journal:
Trans. Amer. Math. Soc. **275** (1983), 357-372

MSC:
Primary 46E27; Secondary 26B30, 28A33, 60B10

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678356-9

MathSciNet review:
678356

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Abstract: Let be a positive integer and let denote the -cube. Let denote the (sup norm) space of continuous (real-valued) functions defined on , and let denote the (variation norm) space of (real-valued) signed Borel measures defined on the Borel subsets of . Let be a sequence of elements of . Necessary and sufficient conditions are given in order that exists for every . After considering a finite dimensional case, the infinite dimensional case is entertained.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678356-9

Article copyright:
© Copyright 1983
American Mathematical Society