One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through problem situations and explanatory materials. In this volume, an algebra of sets is defined, and probability measures on algebras considered. These concepts are generalized to the concept of measure space. Borel sets, measurable functions, and integration of measurable functions are studied. Product measures are defined. (SD)