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 and the sets of functions that are Itô-belated and Lebesgue integrable on [*a, b*). It is known that , so the assertion in the title is substantiated by showing that in the sequel.

**[1]**Ralph Henstock,*A Riemann-type integral of Lebesgue power*, Canad. J. Math.**20**(1968), 79–87. MR**0219675****[2]**Jaroslav Kurzweil,*Generalized ordinary differential equations and continuous dependence on a parameter*, Czechoslovak Math. J.**7 (82)**(1957), 418–449 (Russian). MR**0111875****[3]**E. J. McShane and T. A. Botts,*A modified Riemann-Stieltjes integral*, Duke Math. J.**19**(1952), 293–302. MR**0047746****[4]**E. J. McShane,*A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals*, Memoirs of the American Mathematical Society, No. 88, American Mathematical Society, Providence, R.I., 1969. MR**0265527****[5]**E. J. McShane,*Stochastic calculus and stochastic models*, Academic Press, New York-London, 1974. Probability and Mathematical Statistics, Vol. 25. MR**0443084**

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0507321-0

Keywords:
Itô-belated integral,
Lebesgue integral

Article copyright:
© Copyright 1978
American Mathematical Society