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Singular Integrals are Perron Integrals of a Certain Type

Published online by Cambridge University Press:  20 November 2018

W. F. Pfeffer
W. F. Pfeffer*
Affiliation:
University of California, Berkeley, California
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In [7] a Perron-like integral was denned in an arbitrary topological space and many of its basic properties were established. In this paper we shall show (the theorem in § 2) that in a suitable setting the integral from [7] includes a class of so-called singular integrals, i.e., generalized forms of the Cauchy principal value of an integral. Thus, the powerful machinery of Perron integration, e.g., the monotone and dominant convergence theorems, can be automatically applied to these singular integrals.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 2 , 01 April 1970 , pp. 260 - 264
Copyright
Copyright © Canadian Mathematical Society 1970

References

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