I shall describe the use of Poissonization methods in large
sample theory. I shall put special emphasis on those developed and
spotlighted in my 2003 joint work with my colleagues Evarist Gine and
Andrei Zaitsev. Then I shall discuss their application to the
derivation of the asymptotic distribution of a kernel estimator of level
sets of densities and the exact limit behavior of the Lp loss of kernel
density estimators. The application part of my talk is largely based
upon two papers in progress with Wolfgang Polonik and Boris Levit.
