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In this paper, we prove that fg is Henstock integrable on an interval in the Euclidean space for each Henstock integrable function / if and only if g is a function of essentially strongly bounded variation.

Using Henstock variational measures, new Fubini-Tonelli type theorems are established for the Henstock-Kurzweil integral. In particular, we extend a result of Henstock.  2004 Elsevier Inc. All rights reserved.

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This paper is a continuation of the paper [T.Y. Lee, Product variational measures and Fubini-Tonelli type theorems for the Henstock-Kurzweil integral, J. Math. Anal. Appl. 298 (2004) 677-692], in which we proved several Fubini-Tonelli type theorems for the Henstock-Kurzweil integral. Let f be Henstock-Kurzweil integrable on a compact interval r i=1 [a i , b i ] ⊂ R r . For a given compact interval s j =1 [c j , d j ] ⊂ R s , set T f s j =1