Klebert Kentia (HU Berlin)

2010/11/19, 16:00

FU Berlin, at room SR 031 (Arnimallee 6)

Multifunctions, or multivalued mappings or correspondences, are “functions” that assign to a fixed point one or several values. They can be viewed as set-valued mappings and turn out to be very interesting objects in many areas of mathematics (e.g. optimization, probability, functional analysis). This motivates the need for a nice and thorough analysis of these objects. During this analysis, some questions arise when one indeed considers correspondences as mappings taking values in the power set of a given set. Of particular importance is how one defines a useful (mainly in application) concept of measurability (i.e. conservation of information by inverse image) for such mappings. If this is at all possible, then can one associate to a measurable correspondence a suitable notion of integral? An even more interesting question is that of the existence of a measurable selection of a correspondence (i.e. a measurable function that takes values in the values of the correspondence). The purpose of this talk will be to attempt to address some of these questions.