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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Current valued measures and Geöcze area


Author: Ronald Gariepy
Journal: Trans. Amer. Math. Soc. 166 (1972), 133-146
MSC: Primary 28A75
MathSciNet review: 0293066
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Abstract: If f is a continuous mapping of finite Geöcze area from a polyhedral region $ X \subset {R^k}$ into $ {R^n},2 \leqq k \leqq n$, then, under suitable hypotheses, one can associate with f, by means of the Cesari-Weierstrass integral, a current valued measure T over the middle space of f. In particular, if either $ k = 2$ or the $ k + 1$-dimensional Hausdorff measure of $ f(X)$ is zero, then T is essentially the same as a current valued measure defined by H. Federer and hence serves to describe the tangential properties of f and the multiplicities with which f assumes its values. Further, the total variation of T is equal to the Geöcze area of f.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0293066-0
PII: S 0002-9947(1972)0293066-0
Keywords: Current valued measures, Geöcze area, Cesari-Weierstrass integral, k-vector valued density, Hausdorff measure
Article copyright: © Copyright 1972 American Mathematical Society