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Proceedings of the American Mathematical Society

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$ \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: 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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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

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