  In this paper we show that Markov uniqueness for symmetric pre-Dirichlet
operators $L$ follows from the uniqueness of the corresponding
Fokker-Planck-Kolmogorov equation (FPKE). Since in recent years a considerable
number of uniqueness results for FPKE's have been achieved, we obtain new
Markov uniqueness results in concrete cases. A selection of such will be
presented in this paper. They include cases with killing and with degenerate
diffusion coefficients.
