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For 0 < q < 1 and 0 < α < 1, we construct the infinite dimensional q-Gamma white noise measure γα,q by using the Bochner-Minlos theorem. Then we give the chaos decomposition of an L2 space with respect to the measure γα,q via an isomorphism with the 1-mode type interacting Fock space associated to the q-Gamma measure.doi:10.1515/tmmp-2016-0022 fatcat:th3lh6gu2feyvhhqvneymxqh3e