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Continuity of the integral as a function of the domain

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Abstract

We present here the fundamentals of a theory of domains that offers unifying techniques and terminology for a number of different fields. Using direct, geometric methods, we develop integration over p-dimensional domains in n-dimensional Euclidean space ⩄n, replacing the method of parametrization of a domain with the method of approximation in Banach spaces. We prove basic results needed for a theory of integration — continuity of the integral as a function of its domain and integrand (Corollary 4.8) and a generalization of Stokes’s theorem (Corollary 4.14).

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley

    Jenny Harrison

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  1. Jenny Harrison
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Correspondence to Jenny Harrison.

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Harrison, J. Continuity of the integral as a function of the domain. J Geom Anal 8, 769–795 (1998). https://doi.org/10.1007/BF02922670

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  • DOI: https://doi.org/10.1007/BF02922670

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