  We study integrability and equivalence of L^p-norms of polynomial chaos
elements. Relying on known results for Banach space valued polynomials, a
simple technique is presented to obtain integrability results for random
elements that are not necessarily limits of Banach space valued polynomials.
This enables us to prove integrability results for a large class of seminorms
of stochastic processes and to answer, partially, a question raised by C.
Borell (1979, Seminaire de Probabilites, XIII, 1-3).
