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The deterministic Itô-belated integral is equivalent to the Lebesgue integral


Authors: R. B. Darst and E. J. McShane
Journal: Proc. Amer. Math. Soc. 72 (1978), 271-275
MSC: Primary 26A42
MathSciNet review: 507321
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Abstract: Let [a, b) be a bounded half-open interval in the real numbers R. Denote by $ \mathcal{I} = \mathcal{I}[a,b)$ and $ \mathcal{L} = \mathcal{L}[a,b)$ the sets of functions $ f:R \to R$ that are Itô-belated and Lebesgue integrable on [a, b). It is known that $ \mathcal{L} \subset \mathcal{I}$, so the assertion in the title is substantiated by showing that $ \mathcal{I} \subset \mathcal{L}$ in the sequel.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507321-0
Keywords: Itô-belated integral, Lebesgue integral
Article copyright: © Copyright 1978 American Mathematical Society