  In this paper we study Markov chains associated with the Metropolis-Hastings
algorithm. We consider conditions under which the sequence of the successive
densities of such a chain converges to the target density according to the
total variation distance for any choice of the initial density. In particular
we prove that the positiveness of the proposal density is enough for the chain
to converge. The content of this work basically presents a stand alone proof
that the reversibility along with the kernel positivity imply the convergence.
