Mathematics (Nov 2022)
Constructing a Linearly Ordered Topological Space from a Fractal Structure: A Probabilistic Approach
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.
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