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Change of variable in the one-dimensional Lebesgue integral

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Abstract

We obtain necessary and sufficient conditions for the change of the variable in a one-dimensional Lebesgue integral in the case when the substituting function is quasibijective (see Definition 1).

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Literature cited

  1. P. de Lucia, “Sulla caratterizzazione delle funzioni numeriche di una variabile quasi ovunque derivabili rispetto ad un'altra,” Ricerche Mat.,19, No. 1, 26–47 (1970).

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  2. D. E. Varberg, “Change of variables in multiple integrals,” Amer. Math. Monthly,78, No. 1, 42–45 (1971).

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  3. S. Saks, Theory of the Integral, Hafner, New York (1937).

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Authors and Affiliations

  1. V. I. Lenin Moscow State Pedagogical Institute, USSR

    V. Orlov

Authors
  1. V. Orlov
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Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 747–758, May, 1973.

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Orlov, V. Change of variable in the one-dimensional Lebesgue integral. Mathematical Notes of the Academy of Sciences of the USSR 13, 446–452 (1973). https://doi.org/10.1007/BF01147476

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  • DOI: https://doi.org/10.1007/BF01147476

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