Many models for various modal logics have been given over the years. Recently the author noticed that the complete Boolean algebra of measurable subsets of the unit interval modulo sets of measure zero retains a topological structure. This is possible because working modulo null sets does not always identify open and closed sets. Therefore, a non-trivial Boolean-valued model of the Lewis modal system S4 is obtained. For this presentation a simplified description of semantics for a rich second-order system will be given together with a discussion of why this model is worth further consideration. Inasmuch as the semantics gives every proposition a well defined probability, we may find some new insights about modeling randomness.