Negligible Variation and the Change of Variables Theorem

Negligible Variation and the Change of Variables Theorem

In this note we prove a necessary and sufficient condition for the change of variables formula for the HK integral, with implications for the change of variables formula for the Lebesgue integral. As a corollary, we obtain a necessary and sufficient condition for the Fundamental Theorem of Calculus...

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Veröffentlicht in:Indiana University mathematics journal 2012-01, Vol.61 (1), p.31-44
Hauptverfasser: Rutherfoord, Vermont, Sagher, Yoram
Format: Artikel
Sprache:eng
Schlagworte:
Closed intervals
Fundamental theorem of calculus
Mathematical functions
Mathematical integrals
Mathematical integration
Mathematical intervals
Mathematical theorems
Null set
Sufficient conditions
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Zusammenfassung:In this note we prove a necessary and sufficient condition for the change of variables formula for the HK integral, with implications for the change of variables formula for the Lebesgue integral. As a corollary, we obtain a necessary and sufficient condition for the Fundamental Theorem of Calculus to hold for the HK integral.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2012.61.4532