Geöcze area and a convergence property

Author:
Ronald Gariepy

Journal:
Proc. Amer. Math. Soc. **34** (1972), 469-474

MSC:
Primary 28A75; Secondary 26A63

DOI:
https://doi.org/10.1090/S0002-9939-1972-0297974-1

MathSciNet review:
0297974

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose *f* is a continuous mapping with finite Lebesgue area from a polyhedral region into . Let be the monotone-light factorization of *f* with middle space *M*.

If *f* satisfies a ``cylindrical condition'' considered by T. Nishiura, then a current valued measure *T* over *M* can be associated with *f* by means of the Cesari-Weierstrass integral, and if is any sequence of quasi-linear maps converging uniformly to *f* with bounded areas, then

*k*-form in and

*g*is a continuous real valued function on

*M*which vanishes on Bdry.

The total variation measure of *T*, taken with respect to mass, coincides with the Geöcze area measure over *M*.

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DOI:
https://doi.org/10.1090/S0002-9939-1972-0297974-1

Article copyright:
© Copyright 1972
American Mathematical Society