  The paper proposes a notion of volume element for Finsler spaces with metrics
of Lorentzian signature, equipped with a time orientation. This notion is based
on a slight modification of the idea of Holmes-Thompson volume element working
for positive definite Finsler metrics and can be used in field-theoretical
applications on a Finslerian background. Though the approach assumes the
existence of a time orientation, the volume element does not depend on its
choice.
