  The solvability in Sobolev spaces with special mixed norms is proved for
nondivergence form second order parabolic equations. The leading coefficients
are assumed to be measurable in the time variable and two coordinates of space
variables, and be almost in VMO (vanishing mean oscillation) with respect to
the other coordinates. This solvability result implies the weak uniqueness of
solutions of the corresponding stochastic It\^o equations in the class of
"good" solutions (which is nonempty). This also implies uniqueness of a Green's
function in the class of "good" ones (which is always nonempty).
