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A Remark on the Change of Variable Theorem for the Riemann Integral

Author

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  • Alexander Kuleshov

    (Department of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, 119991 Moscow, Russia)

Abstract

In 1961, Kestelman first proved the change in the variable theorem for the Riemann integral in its modern form. In 1970, Preiss and Uher supplemented his result with the inverse statement. Later, in a number of papers (Sarkhel, Výborný, Puoso, Tandra, and Torchinsky), the alternative proofs of these theorems were given within the same formulations. In this note, we show that one of the restrictions (namely, the boundedness of the function f on its entire domain) can be omitted while the change of variable formula still holds.

Suggested Citation

  • Alexander Kuleshov, 2021. "A Remark on the Change of Variable Theorem for the Riemann Integral," Mathematics, MDPI, vol. 9(16), pages 1-4, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1899-:d:611362
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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

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