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:arXiv.org 2012-12
Hauptverfasser: Rutherfoord, Vermont, Sagher, Yoram
Format: Artikel
Sprache:eng
Schlagworte:
Calculus
Integrals
Theorems
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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:2331-8422