Properties of high redshift clusters are a fundamental source of
information for cosmology. In particular, the combined knowledge of the redshift distribution of X-ray clusters of
galaxies and the
luminosity-temperature correlation, $L_X-T_X$, provides a powerful test of
the mean density of the Universe. We will address the question
of the possible evolution of this relation from an observational point
of view and its cosmological
significance using a new indicator to measure the evolution of the X-ray
luminosity-temperature relation
with redshift. This new indicator is applied to a significant number of high and intermediate redshift X-ray clusters of galaxies. We find a slightly positive
evolution in the $L_X-T_X$ relation.
This implies a high value of the density parameter of $0.85\pm0.2 $.