Lévy white noise measures on infinite-dimensional spaces: Existence and characterization of the measurable support

It is shown that a Lévy white noise measure Λ always exists as a Borel measure on the dual K′ of the space K of C∞ functions on R with compact support. Then a characterization theorem that ensures that the measurable support of Λ is contained in S′ is proved. In the course of the proofs, a representation of the Lévy process as a function on K′ is obtained and stochastic Lévy integrals are studied.