We study the Nikodym property for Boolean algebras. The property is closely related to the barrelledness of the subspace of \(C(St(\mathcal {A}))\) , where \(St(\mathcal {A})\) denotes the Stone space of a Boolean algebra \(\mathcal {A}\) , spanned by the set of all characteristic functions corresponding via the Stone duality to elements of \(\mathcal {A}\) and hence, to the classical Banach–Steinhaus theorem. We present a proof of Nikodym’s uniform boundedness theorem asserting that every \(\sigma \) -complete Boolean algebra has the Nikodym property. Finally, we introduce the strong Nikodym property, a strengthening of the previous property, and show a proof of Valdivia’s result asserting that every \(\sigma \) -field has the strong Nikodym property.