Memoirs of the American Mathematical Society 2009; 101 pp; softcover Volume: 199 ISBN10: 0821843184 ISBN13: 9780821843185 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/199/930
 In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying \(E_0\)semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in \([0,1]\) or \(\mathbb R_+\). These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types \(\mathrm{I}_n\), \(\mathrm{II}_n\) and \(\mathrm{III}\) is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant. Table of Contents  Introduction
 Basics
 From product systems to random sets
 From random sets to product systems
 An hierarchy of random sets
 Direct integral representations
 Measurability in product systems: An algebraic approach
 Construction of product systems from general measure types
 Beyond separability: Random bisets
 An algebraic invariant of product systems
 Conclusions and outlook
 Bibliography
