  In this paper, we show that there is a one-to-one correspondence between
operator monotone functions on the nonnegative reals and finite Borel measures
on the unit interval. This correspondence appears as an integral representation
of special operator monotone functions $x \mapsto 1\,!_t\,x$ for $t \in [0,1]$
with respect to a finite Borel measure on $[0,1]$, here $!_t$ denotes the
$t$-weighted harmonic mean. Hence such functions form building blocks for
arbitrary operator monotone functions on the nonnegative reals. Moreover, we
use this integral representation to decompose operator monotone functions.
