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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ \lambda$-power integrals on the Cantor type sets


Author: Shushang Fu
Journal: Proc. Amer. Math. Soc. 123 (1995), 2731-2737
MSC: Primary 26A24; Secondary 26A39
MathSciNet review: 1257105
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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the notions of $ \lambda $-power dyadic derivatives and $ \lambda $-power dyadic integrals, so that, in particular, the Cantor ternery function is an indefinite integral of its derivative. Furthermore, under certain conditions on the integrands we can give a Riemann-type definition to the $ \lambda $-power dyadic integral.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1257105-3
PII: S 0002-9939(1995)1257105-3
Keywords: Singular function, Cantor type set, Hausdorff dimension and Hausdorff measure, $ \lambda $-power dyadic derivative, $ \lambda $-power dyadic integral, $ \lambda $-power Riemann integral
Article copyright: © Copyright 1995 American Mathematical Society