Bulletin of the American Mathematical Society

The Kolmogoroff principle for the Lebesgue area

R. G. Helsel and E. J. Mickle

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 54, Number 2 (1948), 235-238.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183511694

Mathematical Reviews number (MathSciNet)
MR0023891

Zentralblatt MATH identifier
0031.29301

Citation

Helsel, R. G.; Mickle, E. J. The Kolmogoroff principle for the Lebesgue area. Bull. Amer. Math. Soc. 54 (1948), no. 2, 235--238. https://projecteuclid.org/euclid.bams/1183511694


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References

  • 1. R. G. Helsel, A theorem on surface area, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 443-453.
  • 2. M. D. Kirszbraun, Über die zusammenziehende und Lipschitzsche Transformationen, Fund. Math. vol. 22 (1934) pp. 77-108.
  • 3. A. Kolmogoroff, Beitrage zur Masstheorie, Math. Ann. vol. 107 (1933) pp. 351-366.
  • 4. H. Rademacher, Über partielle und totale Differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale, Math. Ann. vol. 79 (1918) pp. 340-359.
  • 5. T. Radó, Über das Flächenmass rektifizierbarer Flächen, Math. Ann. vol. 100 (1928) pp. 445-479.
  • 6. P. V. Reichelderfer, The effect of a Lipschitzian transformation on the area of a continuous surface. Bull. Amer. Math. Soc. Abstract 53-5-225.
  • 7. J. W. T. Youngs, The additivity of the Lebesgue area, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 779-784.

See also

  • This work is cited by: Earl J. Mickle. On the extension of a transformation. Bull. Amer. Math. Soc., Volume 55, Number 2 (1949), 160--164.