Acta Mathematica

Lebesgue area of maps from Hausdorff spaces

R. F. Williams

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This research was begun while the author was a member of the Seminar on Surface Area, led by L. Cesari at Purdue University, and completed while he held an XL fellowship from the Purdue Research Foundation.

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Acta Math., Volume 102, Number 1-2 (1959), 33-46.

First available in Project Euclid: 31 January 2017

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1959 © Almqvist & Wiksells Boktryckeri


Williams, R. F. Lebesgue area of maps from Hausdorff spaces. Acta Math. 102 (1959), no. 1-2, 33--46. doi:10.1007/BF02559567.

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  • L. Cesari, Su di un teorrema di T. Radó sulla transformazioni continue, Atti del Reale Instituto Veneto di Scienze, Lettere ed Arti, Tom CI, Parte II (1942), 337–403.
  • L. Cesari, Surface Area, Annals of Mathematics Studies, no. 35, Princeton Univ. Press. 1956.
  • S. Eilenberg & N. Steenrod, Foundations of Algebraic Topology. Princeton Math. Series no. 15, Princeton, 1952.
  • H. Federer, Essential Multiplicity and Lebesgue area. Proc. Nat. Acad. Sci., 34 (1948), 611–616.
  • —, On Lebesgue area. Ann. of Math., 61, no. 2 (1955), 289–353.
  • W. Hurewicz & H. Wallman, Dimension Theory. Princeton Math. Series no. 4, Princeton, 1948.
  • T. Radó, Length and Area. Amer. Math. Soc. Coll. Publications, vol. XXX, 1948.
  • T. Radó & P. Reichelderfer, Continuous transformations in Analysis, Grundlehren der Mathematischen Wissenschaften, vol. 75. Berlin, Springer 1955.