<P> Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects . Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics . The language of set theory can be used in the definitions of nearly all mathematical objects . </P> <P> The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s . After the discovery of paradoxes in naive set theory, such as the Russell's paradox, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo--Fraenkel axioms, with or without the axiom of choice, are the best - known . </P> <P> Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo--Fraenkel set theory with the axiom of choice . Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community . Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals . </P>

Who developed the set theory approach to probability