Negligible Variation and the Change of Variables Theorem

2012/12/19 by Vermont Rutherfoord, Rutherfoord, Vermont, Yoram Sagher +1
Mathematics · #26A36 #26A39 #26A46 (Primary) 26A30 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A30 #msc:26A36 #msc:26A39 #msc:26A46

paper · pdf · doi:10.48550/arxiv.1212.4574

arxiv created 2012/12/19 · arxiv updated 2012/12/20

Abstract

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.

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