$D$-posets introduced by F. Chovanec and F. K\^ opka ten years ago
provide a suitable algebraic structure to model events in
probability theory. Generalizing analogous results for fields of
sets and bold algebras, we describe a duality between certain
coproducts of $D$-posets and generalized measurable spaces. An
important role in the duality is played by sequential convergence.
We mention some applications to the foundations of probability.
