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A note on Henstock- Itô's non-stochastic integral
Citation
Lim, C. Y. Y., & Toh, T. L. (2022). A note on Henstock-Itô's non-stochastic integral. Real Analysis Exchange, 47(2), 443-460. https://doi.org/10.14321/realanalexch.47.2.1637314733
Abstract
It is well-known that the generalized Riemann approach using non-uniform mesh has given rise to integrals which are more general than the Riemann integral. In this note, motivated by earlier studies on stochastic integrals, we consider special interval-point pair in defining the Riemann sum, where the point (or the tag) is the left-hand point of the interval. We show that this approach in fact is equivalent to the Lebesgue integral. Hence this simplifies McShane's construction of interval-point pair. Moreover, by restricting to the tag as the left hand point of the interval, the integration-by-substitution and by-parts formulae become easy consequences of the definition.
Date Issued
2022
Publisher
Michigan State University
Journal
Real Analysis Exchange