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Absolute continuity on tracks and mappings of Sobolev spaces

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Bibliography

  1. Calkin, J. W., Functions of several variables and absolute continuity I. Duke Math. J. 6, 170–186 (1940).

    Google Scholar 

  2. Federer, H., Geometric Measure Theory (Grundlehren d. Math. Wiss., Vol. 153). New York: Springer (1969).

    Google Scholar 

  3. Gagliardo, E., Proprietà di alcune classi di funzioni in più variabili. Richerche di Mat. 7, 102–137 (1958).

    Google Scholar 

  4. Morrey, C. B., Functions of several variables and absolute continuity II. Duke Math. J. 6, 187–215 (1940).

    Google Scholar 

  5. Roger, F., Sur la relation entre les propriétés tangentielles et metriques des ensembles cartésiens. C. R. Acad. Sci. Paris 201, 871–872 (1935).

    Google Scholar 

  6. Saks, S., Theory of the Integral. Second ed. (Monografje Math., Vol. 7) Warsaw, 1937. Reprinted Stechert-Hafner Pub. Co., New York. New York: Dover 1964.

    Google Scholar 

  7. Serrin, J., Personal communication, 1971.

  8. Serrin, J., & D. E. Varberg, A general chain rule for derivatives and the change of variables formula for the Lebesgue integral. Amer. Math. Monthly 76, 514–520 (1969)

    Google Scholar 

  9. Sobolev, S. L., Applications of Functional Analysis in Mathematical Physics (Transl, of Math. Monographs, Vol. 7). Providence, Amer. Math. Soc., 1963.

    Google Scholar 

  10. Vallée Poussin, Ch. J. de la, Sur l'intégrale de Lebesgue. Trans. Amer. Math. Soc. 16, 435–501 (1915).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Technion, Haifa, Israel

    M. Marcus & V. J. Mizel

  2. Department of Mathematics, Carnegie-Mellon University, Pittsburgh

    M. Marcus & V. J. Mizel

Authors
  1. M. Marcus
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  2. V. J. Mizel
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Communicated by J. Serrin

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Marcus, M., Mizel, V.J. Absolute continuity on tracks and mappings of Sobolev spaces. Arch. Rational Mech. Anal. 45, 294–320 (1972). https://doi.org/10.1007/BF00251378

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  • DOI: https://doi.org/10.1007/BF00251378

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