Constructing a Linearly Ordered Topological Space from a Fractal Structure: A Probabilistic Approach

José Fulgencio Gálvez-Rodríguez () and Miguel Ángel Sánchez-Granero ()
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José Fulgencio Gálvez-Rodríguez: Department of Mathematics, Universidad de Almería, 04120 Almería, Spain
Miguel Ángel Sánchez-Granero: Department of Mathematics, Universidad de Almería, 04120 Almería, Spain

Mathematics, 2022, vol. 10, issue 23, 1-17

Abstract: Recent studies have shown that it is possible to construct a probability measure from a fractal structure defined on a space. On the other hand, a theory on cumulative distribution functions from an order on a separable linearly ordered topological space has been developed. In this paper, we show how to define a linear order on a space with a fractal structure, so that these two theories can be used interchangeably in both topological contexts.

Keywords: probability; measure; fractal structure; cumulative distribution function; linearly ordered topological space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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