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Decomposition of functions whose partial derivatives are measures

Published online by Cambridge University Press:  26 February 2010

Casper Goffman
Casper Goffman
Affiliation:
Purdue University and Westfield College, London.
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Extract

In recent years, functions of n variables whose partial derivatives are measures, have been found to retain the properties of functions of bounded variation of one variable to a remarkable degree [e.g., G1, G2, G3, K, Z, and especially the announcement F].

Type
Research Article
Information
Mathematika , Volume 15 , Issue 2 , December 1968 , pp. 149 - 152
Copyright
Copyright © University College London 1968

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References

F.Federer, H., “Some properties of distributions whose partial derivatives are representable by integration”, Bull. Amer. Math. Soc., 74 (1968), 183–186.CrossRefGoogle Scholar
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G2.Goffman, C., “Non-parametric surfaces given by linearly continuous functions”, Ada. Math., 103 (1960), 269–291.Google Scholar
G3.Goffman, C., “A characterization of linearly continuous functions whose partial derivatives are measures”, Ada Math., 117 (1967), 165–190.Google Scholar
K.Krickeberg, K., “Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nichtparametrischer Flächen”, Ann. Mat. Pura Appl. IV, 44 (1957), 105–133.CrossRefGoogle Scholar
Z.Ziemer, W., “The area and variation of linearly continuous functions”, Proc. Amer. Math. Soc., to appear.Google Scholar