We show that the following are dual: the category whose
objects are Boolean algebras carrying the initial sequential
convergence  with respect to the sequentially continuous
homomorphisms into the two-element Boolean algebra and whose
morphisms are sequentially continuous homomorphisms and the
category whose objects are reduced $s$-perfect fields of
sets (ultrafilters having the countable intersection
property are fixed) and whose morphisms are measurable maps.
The motivation comes from the foundations of probability:
$s$-perfect fields of sets have good categorical properties
and yield a suitable model for the field of events. The
duality covers the nontopological Stone duality between
Boolean algebras and reduced perfect fields of sets as a
special case. Indeed, the category of Boolean algebras is
isomorphic to the category of Boolean algebras carrying the
initial sequential convergence with respect to all
homomorphisms into the two-element Boolean algebra.