ABSTRACT
Conditioning as a functional analysis concept has applications not
only in probability but also in many other contexts in modern analysis.
In this chapter some of these ideas are discussed showing in particu-
lar that they are well-suited as (subMarkov) kernels in extending the
classical potential theory, analyzing bistochastic operators as well as
Reynolds operators arising in turbulence theory, and elsewhere. Also
it is shown how conditional expectation operators can be used as mod-
els for describing general (contractive) projections in many function
spaces. Almost all these applications are based on regular conditional
measures, and the theory is then executed from the “idealistic” view.
10.1 Introduction and motivation
