ON THE SUPPORT OF THE ASHTEKAR-LEWANDOWSKI MEASURE

We show that the Ashtekar-Isham extension ($) over bar A/G of the conf iguration space of Yang-Mills theories A/G is (topologically and measu re-theoretically) the projective limit of a family of finite dimension al spaces associated with arbitrary finite lattices. These results are then used to prove that A/G is contained in a zero measure subset of ($) over bar A/G with respect to the diffeomorphism invariant Ashtekar -Lewandowski measure on ($) over bar A/G. Much as in scalar field theo ry, this implies that states in the quantum theory associated with thi s measure can be realized as functions on the ''extended'' configurati on space ($) over bar A/G.