  In the semigroup approach to stochastic evolution equations, the fundamental
issue of uniqueness of mild solutions is often "reduced" to the much easier
problem of proving uniqueness for strong solutions. This reduction is usually
carried out in a formal way, without really justifying why and how one can do
that. We provide sufficient conditions for uniqueness of mild solutions to a
broad class of semilinear stochastic evolution equations with coefficients
satisfying a monotonicity assumption.
