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Entropies of Sets of Functions of Bounded Variation

Published online by Cambridge University Press:  20 November 2018

G. F. Clements
G. F. Clements*
Affiliation:
Syracuse University
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In this paper the entropies of several sets of functions of bounded variation are calculated. The entropy of a metric set, a notion first introduced by Kolmogorov in (2), is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2∊ necessary to cover it. Using this notion, Kolmogorov (4; p. 357) and Vituškin (7) have shown that not all functions of n variables can be represented by functions of fewer variables if only functions satisfying certain smoothness conditions are allowed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 422 - 432
Copyright
Copyright © Canadian Mathematical Society 1963

References

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