This is Klebert Kentia's talk "What is ... a multifunction?" at the "What is ...?" seminar. The talk was given on Friday, November 19, 4pm at FU Arnimallee 6, SR 031.
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.
For more "What is ...?" seminar videos, visit math.fu-berlin.de/w/Math/WhatIsSeminar.