Functions and Analysis


Apparent Measure and Relative Dimension

Authors: Faycal Ben Adda

In this paper, we introduce a concept of "apparent" measure in R^n and we define a concept of relative dimension (of real order) with it, which depends on the geometry of the object to measure and on the distance which separates it from an observer. At the end we discuss the relative dimension of the Cantor set. This measure enables us to provide a geometric interpretation of the Riemann-Liouville's integral of order alpha between 0 and 1.

Comments: 24 Pages. A short version of this paper was published in Journal Européen des Systèmes Automatisés, Fractional order systems, 42, p733-746, 2008.

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[v1] 2012-03-20 07:02:58

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