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(This is a report for the Proceedings of ``Journees Relativistes 1993''written in September 1993. Containes a short description of the resultspublished elsewhere in the joint paper with A. Ashtekar) Integral calculus onthe space of gauge equivalent connections is developed. By carring out anon-linear generalization of the theory of cylindrical measures on topologicalvector spaces, a faithfull, diffeomorphism invariant measure is introduced on asuitable completion of the quotient space. The strip (i.e. momentum) operatorsare densely-defined in the resulting Hilbert space and interact with themeasure correctly, to become essentially self adjoint operators.Comment: 3 pp., Proceedings of ``Journees Relativistes 1993'

TOPOLOGICAL MEASURE AND GRAPH-DIFFERENTIAL GEOMETRY ON THE QUOTIENT SPACE OF CONNECTIONS