Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On bounded variation and absolute continuity for parametric representations of continuous surfaces

Author: Paul V. Reichelderfer
Journal: Trans. Amer. Math. Soc. 53 (1943), 251-291
MSC: Primary 27.2X
MathSciNet review: 0007917
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [P] Franklin and N. Wiener 1. Analytic approximations to topological transformations, Trans. Amer. Math. Soc. vol. 28 (1926) pp. 762-785. MR 1501373
  • [Z] de Geöcze 1. Quadrature des surfaces courbes, Mathematische und naturwissenschaftliche Berichte aus Ungarn vol. 26 (1908) pp. 1-88.
  • [G] H. Hardy, J. E. Littlewood, G. Polya 1. Inequalities, Cambridge, 1934. MR 0046395 (13:727e)
  • [B] von Kerékjártó 1. Vorlesungen über Topologie, vol. 1, Berlin, 1923.
  • [C] Kuratowski 1. Topologie. I, Warsaw-Lwów, 1933.
  • [T] Rado 1. Sur l'aire des surfaces courbes, Acta Univ. Szeged vol. 3 (1927) pp. 131-169.
  • [2] -Über das Flächenmass rektifizierbarer Flächen, Math. Ann. vol. 100 (1928), pp. 445-479. MR 1512495
  • [3] -On the problem of Plateau, Ergebnisse der Mathematik und ihrer Grenzgebiete, Berlin, 1933.
  • [4] -A lemma on the topological index, Fund. Math. vol. 27 (1936) pp. 212-225.
  • [T] Rado and P. Reichelderfer 1. A theory of absolutely continuous transformations in the plane, Trans. Amer. Math. Soc. vol. 49 (1941) pp. 258-307. MR 0003698 (2:257a)
  • [2] -On convergence in length and convergence in variation, accepted for publication by the Duke Math. J.
  • [S] Saks 1. Theory of the integral, Warsaw-Lwów, 1937.
  • [L] Tonelli 1. Sulla quadratura delle superficie, Rendiconti delle sedute della reale accademia nazionale dei Lincei, Classe di Scienze fisiche, matematiche e naturali, vol. 3 (1926) pp. 357-362; pp. 445-450; pp. 633-638.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 27.2X

Retrieve articles in all journals with MSC: 27.2X

Additional Information

Article copyright: © Copyright 1943 American Mathematical Society

American Mathematical Society