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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the integrals of Perron type

Authors: P. S. Bullen and C. M. Lee
Journal: Trans. Amer. Math. Soc. 182 (1973), 481-501
MSC: Primary 26A39
MathSciNet review: 0338291
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Abstract: An abstract derivate system is defined axiomatically, and then a naturally corresponding Perron integral theory is developed, unifying all the existing integral theories of Perron type of first order. A new scale of approximately mean-continuous integrals and a new scale of symmetric Cesàro-Perron integrals are obtained as examples of the general theory. Also, the MZ-integral and the SCP-integral are proved to be equivalent.

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Keywords: Base, base mappings, lower derivate operator, derivative, legitimate mapping, inequality property, derivate system, major function, minor function, Perron integral, Cesàro-Perron integral, approximately mean-continuous integral, symmetric Cesàro-Perron integral, MZ-integral, SCP-integral
Article copyright: © Copyright 1973 American Mathematical Society

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