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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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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Keywords: Sum integrals, product integrals, subdivision-refinement type integrals, equivalence of integrals
Article copyright: © Copyright 1973 American Mathematical Society