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arXiv · 1912.11452

Median pretrees and functions of bounded variation

Michael Megrelishvili
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Abstract

We introduce functions of bounded variation on median algebras and study some properties for median pretrees. We show that if $X$ is a compact median pretree in its shadow topology then every function $f: X \to R$ of bounded variation has the point of continuity property (Baire 1, if $X$, in addition, is metrizable). We prove a generalized version of Helly's selection theorem for a sequence of functions with total bounded variation defined on a compact metrizable median pretree $X$.

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Michael Megrelishvili. 2019-12-24. Median pretrees and functions of bounded variation. https://arxiv.org/abs/1912.11452

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