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Transactions of the American Mathematical Society

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Area as the integral of lengths of contours


Author: Raymond Rishel
Journal: Trans. Amer. Math. Soc. 97 (1960), 95-119
MSC: Primary 28.00
DOI: https://doi.org/10.1090/S0002-9947-1960-0118805-2
MathSciNet review: 0118805
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  • [1] J. Cecconi, La disuguaglianza di Cavalieri per la k-area secondo Lebesgue in un n-spazio, Ann. Mat. Pura Appl., Ser. 4 vol. 42 (1956) p. 189. MR 0089892 (19:735a)
  • [2] L. Cesari, Surface area, Annals of Mathematics Studies, Princeton University Press, 1956. MR 0074500 (17:596b)
  • [3] -, Contours of a Frechet surface, Riv. Mat. Univ. Parma vol. 4 (1953) p. 173. MR 0060007 (15:611g)
  • [4] H. Federer, Surface area I, II, Trans. Amer. Math. Soc. vol. 55 (1944) p. 420. MR 0010610 (6:44d)
  • [5] -, Measure and area, Bull. Amer. Math. Soc. vol. 58 (1952) p. 306. MR 0049289 (14:149e)
  • [6] -, On Lebesgue area, Ann. of Math. vol. 61 (1955) p. 289. MR 0067178 (16:683a)
  • [7] -, Curvature measures, Trans. Amer. Math. Soc. vol. 93 (1959) p. 418. MR 0110078 (22:961)
  • [8] M. Frechet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo vol. 22 (1906) p. 1.
  • [9] T. Radó, Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948. MR 0024511 (9:505g)
  • [10] E. Silverman, An intrinsic property for Lebesgue area, Riv. Mat. Univ. Parma vol. 2 (1951) p. 193. MR 0046422 (13:731d)
  • [11] -, An intrinsic inequality for Lebesgue area, Pacific J. Math. vol. 6 (1956) 363. MR 0080138 (18:198g)
  • [12] S. Saks, The theory of the integral, Warsaw, 1937.
  • [13] L. C. Young, Partial area. I, to appear in Riv. Mat. Univ. Parma. MR 0141760 (25:5157)
  • [14] H. Whitney, On totally differentiable smooth functions, Pacific J. Math. vol. 1 (1951) p. 143. MR 0043878 (13:333d)

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DOI: https://doi.org/10.1090/S0002-9947-1960-0118805-2
Article copyright: © Copyright 1960 American Mathematical Society

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