... mathematical point of view, some regularity properties (such as convexity, compactness, purification, and upper-semicontinuity) of the distribution of correspondences and of the integration of correspondences ... Distributions and Expectations of Correspondences 3.1 Introduction The theory of correspondences, which has important applications in a variety of areas (including optimization, control theory and mathematical ... Mas-Colell (1984), Hart, Hildenbrand and Kohlberg (1974), Khan and Sun (1999), Keisler and Sun (2009) and Rustichini and Yannelis (1991) See Sun (1996, 1997) and Keisler and Sun (2009) for examples...