Median pretrees and functions of bounded variation

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 $X$.

13 pages, adding new examples and references