  In this Letter, we study the evolution of the autocovariance function (ACF)
of density field fluctuations in star-forming clouds and thus of the
correlation length $l_c(\rho)$ of these fluctuations, which can be identified
as the average size of the most correlated structures within the cloud.
Generalizing the transport equation derived by Chandrasekhar (1951) for static,
homogeneous turbulence, we show that the mass contained within these structures
is an invariant, i.e. that the average mass contained in the most correlated
structures remains constant during the evolution of the cloud, whatever
dominates the global dynamics (gravity or turbulence).
  We show that the growing impact of gravity on the turbulent flow yields an
increase of the variance of the density fluctuations and thus a drastic
decrease of the correlation length. Theoretical relations are successfully
compared to numerical simulations. This picture brings a robust support to star
formation paradigms where the mass concentration in turbulent star-forming
clouds evolves from initially large, weakly correlated filamentary structures
to smaller, denser more correlated ones, and eventually to small, tightly
correlated prestellar cores. We stress that the present results rely on a pure
statistical approach of density fluctuations and do not involve any specific
condition for the formation of prestellar cores. Interestingly enough, we show
that, under average conditions typical of Milky Way molecular clouds, this
invariant average mass is about a solar mass, providing an appealing
explanation for the apparent universality of the IMF under such environments.
