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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?)

  • [1] Ralph Henstock, A Riemann-type integral of Lebesgue power, Canad. J. Math. 20 (1968), 79-87. MR 0219675 (36:2754)
  • [2] J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 7 (82) (1957), 418-446. MR 0111875 (22:2735)
  • [3] E. J. McShane and T. A. Botts, A modified Riemann-Stieltjes integral, Duke Math. J. 19 (1952), 293-302. MR 0047746 (13:924g)
  • [4] E. J. McShane, A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals, Mem. Amer. Math. Soc., No. 88, 1969. MR 0265527 (42:436)
  • [5] -, Stochastic calculus and stochastic models, Academic Press, New York, 1974. MR 0443084 (56:1457)

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Keywords: Itô-belated integral, Lebesgue integral
Article copyright: © Copyright 1978 American Mathematical Society

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