  We analyze the anomalies of superconducting state within a simple exactly
solvable model of the pseudogap state, induced by fluctuations of
``dielectric'' short range order, for the model of the Fermi surface with
``hot'' patches. The analysis is performed for the arbitrary values of the
correlation length xi_{corr} of this short range order. It is shown that
superconducting energy gap averaged over these fluctuations is non zero in a
wide temperature range above T_c - the temperature of homogeneous
superconducting transition. This follows from the absence of self averaging of
the gap over the random field of fluctuations. For temperatures T>T_c
superconductivity apparently appears in separate regions of space (``drops'').
These effects become weaker for shorter correlation lengths xi_{corr} and the
region of ``drops'' on the phase diagram becomes narrower and disappears for
xi_{corr}-->0, however, for the finite values of xi_{corr} the complete self
averaging is absent.
