Current valued measures and Geöcze area
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- by Ronald Gariepy PDF
- Trans. Amer. Math. Soc. 166 (1972), 133-146 Request permission
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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 133-146
- MSC: Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9947-1972-0293066-0
- MathSciNet review: 0293066