  We consider a three-dimensional weakly interacting Bose gas in the
fluctuation region (and its vicinity) of the normal-superfluid phase transition
point. We establish relations between basic thermodynamic functions: density,
$n(T,\mu)$, superfluid density $n_s(T,\mu)$, and condensate density, $n_{\rm
cnd} (T,\mu)$. Being universal for all weakly interacting $|\psi|^4$ systems,
these relations are obtained from Monte Carlo simulations of the classical
$|\psi|^4$ model on a lattice. Comparing with the mean-field results yields a
quantitative estimate of the fluctuation region size. Away from the fluctuation
region, on the superfluid side, all the data perfectly agree with the
predictions of the quasicondensate mean field theory.--This demonstrates that
the only effect of the leading above-the-mean-field corrections in the
condensate based treatments is to replace the condensate density with the
quasicondensate one in all local thermodynamic relations. Surprisingly, we find
that a significant fraction of the density profile of a loosely trapped atomic
gas might correspond to the fluctuation region.

Superconductivity;Statistical Mechanics