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The significant cylindrical condition and a Hausdorff rectifiable set


Author: J. C. Breckenridge
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
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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.


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  • [1] J. C. Breckenridge, Cesari-Weierstrass surface integrals and lower k-area, Ann. Scuola Norm. Sup. Pisa (2) 25 (1971), 423-446. MR 0315092 (47:3641)
  • [2] -, Geöcze k-area and significant sets, Accad. Naz. Sci. Lett. Arti Modena Atti Mem. (to appear).
  • [3] L. Cesari, Surface area, Ann. of Math. Studies, no. 35, Princeton Univ. Press, Princeton, N.J., 1956. MR 17, 596. MR 0074500 (17:596b)
  • [4] H. Federer, Essential multiplicity and Lebesgue area, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 611-616. MR 10, 361. MR 0027837 (10:361e)
  • [5] -, Currents and area, Trans. Amer. Math. Soc. 98 (1961), 204-233. MR 23 #A1006. MR 0123682 (23:A1006)
  • [6] -, Geometric measure theory, Die Grundlehren der math. Wissenschaften, Band 153, Springer-Verlag, New York, 1969. MR 41 #1976. MR 0257325 (41:1976)
  • [7] T. Nishiura, Integrals over a product variety and Fubini theorems, Rend. Circ. Mat. Palermo (2) 14 (1965), 207-236. MR 33 #5848. MR 0197685 (33:5848)
  • [8] -, Area measure and Radó's lower area, Trans. Amer. Math. Soc. 159 (1971), 355-367. MR 0281880 (43:7594)
  • [9] T. Radó, On multiplicity functions associated with Lebesgue area, Rend. Circ. Mat. Palermo (2) 4 (1955), 219-236. MR 17, 595. MR 0074498 (17:595f)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0311876-4
Keywords: Surface area, area measures
Article copyright: © Copyright 1973 American Mathematical Society

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