We study the space-time dependence of muon pair production from dense,
nonequilibrium pion matter in the framework of a Boltzmann type trans
port model which properly includes effects of Bose statistics. Startin
g from an initially supersaturated pion gas with a large positive effe
ctive chemical potential we find that this pion chemical potential sta
ys approximately constant during the evolution. As a consequence, such
a scenario leads to an increased dilepton yield near the kinematical
threshold for muon pair production via pion annihilation. Depending on
the lifetime of the dense hadron matter formed in relativistic heavy
ion collisions, this component can be observed above the background of
muon pairs from resonance decays and the rho, omega bump. In such a w
ay the measurement of the dimuon invariant mass spectrum could help to
understand the initial state and the dynamical evolution of ultrarela
tivistic heavy ion collisions.