Analysis on a Fractal Set

Details Analysis on a Fractal Set Analysis on a Fractal Set

2010-01-10

arxiv.org/abs/1001.1485v1

Fractals, vol. 17, No. 1, (2009), 45-52

Mathematics

General Mathematics

AMS-Latex 2e, 13 pages, no figures

Scientific paper

The formulation of a new analysis on a zero measure Cantor set $C (\subset I=[0,1])$ is presented. A non-archimedean absolute value is introduced in $C$ exploiting the concept of {\em relative} infinitesimals and a scale invariant ultrametric valuation of the form $\log_{\varepsilon^{-1}} (\varepsilon/x) $ for a given scale $\varepsilon>0$ and infinitesimals $0

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