  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 $X$.
