The significant cylindrical condition and a Hausdorff rectifiable set
HTML articles powered by AMS MathViewer
- by J. C. Breckenridge PDF
- Proc. Amer. Math. Soc. 37 (1973), 549-552 Request permission
Abstract:
Area measures of the Geöcze type can be constructed for continuous parametric surfaces of finite Lebesgue area provided the surface satisfies the significant cylindrical condition. It is shown that requiring this condition is equivalent to requiring the Hausdorff rectifiability of a certain subset of the range of the surface.References
- J. C. Breckenridge, Cesari-Weierstrass surface integrals and lower $k$-area, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 25 (1971), 423–446. MR 315092 —, Geöcze k-area and significant sets, Accad. Naz. Sci. Lett. Arti Modena Atti Mem. (to appear).
- Lamberto Cesari, Surface area, Annals of Mathematics Studies, No. 35, Princeton University Press, Princeton, N. J., 1956. MR 0074500
- Herbert Federer, Essential multiplicity and Lebesgue area, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 611–616. MR 27837, DOI 10.1073/pnas.34.12.611
- Hebert Federer, Currents and area, Trans. Amer. Math. Soc. 98 (1961), 204–233. MR 123682, DOI 10.1090/S0002-9947-1961-0123682-0
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- Togo Nishiura, Integrals over a product variety and Fubini theorems, Rend. Circ. Mat. Palermo (2) 14 (1965), 207–236. MR 197685, DOI 10.1007/BF02847721
- Togo Nishiura, Area measure and Radó’s lower area, Trans. Amer. Math. Soc. 159 (1971), 355–367. MR 281880, DOI 10.1090/S0002-9947-1971-0281880-6
- Tibor Radó, On multiplicity functions associated with Lebesgue area, Rend. Circ. Mat. Palermo (2) 4 (1955), 219–236. MR 74498, DOI 10.1007/BF02849296
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 549-552
- MSC: Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-1973-0311876-4
- MathSciNet review: 0311876