  This paper develops new extremal principles of variational analysis that are
motivated by applications to constrained problems of stochastic programming and
semi-infinite programming without smoothness and/or convexity assumptions.
These extremal principles concern measurable set-valued mappings/multifunctions
with values in finite-dimensional spaces and are established in both
approximate and exact forms. The obtained principles are instrumental to derive
via variational approaches integral representations and upper estimates of
regular and limiting normals cones to essential intersections of sets defined
by measurable multifunctions, which are in turn crucial for novel applications
to stochastic and semi-infinite programming.
