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Equivalence of integrals


Author: J. A. Chatfield
Journal: Proc. Amer. Math. Soc. 38 (1973), 279-285
MSC: Primary 26A39
DOI: https://doi.org/10.1090/S0002-9939-1973-0311847-8
MathSciNet review: 0311847
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Abstract: Suppose $ R$ is the set of real numbers and $ N$ is the set of nonnegative real numbers, each of $ G$ and $ F$ is a function from $ R \times R$ to $ N$. All integrals considered are of the subdivision-refinement type. This paper gives necessary and sufficient conditions for $ \int_a^b {F = } \int_a^b G $. A necessary and sufficient condition for $ \int_a^b {{G^2} = 0} $ is also given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0311847-8
Keywords: Sum integrals, product integrals, subdivision-refinement type integrals, equivalence of integrals
Article copyright: © Copyright 1973 American Mathematical Society

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