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

Alexander Kuleshov
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Alexander Kuleshov: Department of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2021, vol. 9, issue 16, 1-4

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.

Keywords: real analysis; Riemann integral; change of variable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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