Introductory Topics in Binary Set Functions

Abstract

Let X be a non-empty set and U a ring of subsets of X. The countable additive functions U->{0,1} are called measures. The paper gives some definitions (derivable measures, the Lebesgue-Stieltjes measures) and properties of these functions, its purpose being that of reconstruction of the measure theory within this frame, by analogy with the real measure theory. We mention the special case of the Riemann integrals.