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It is known that the $k$-dimensional Hausdorff measure on a $k$-dimensionalsubmanifold of $\mathbb{R}^n$ is closely related to the Lebesgue measure on$\mathbb{R}^n$. We show that the Ashtekar-Lewandowski measure on the space ofgeneralized $G$-connections for a compact, semi-simple, Lie group $G$, isanalogously related to the product measure on the set of all $G$-valuedfunctions on the group of loops. We also show that, the Ashtekar-Lewandowskimeasure is, under very mild conditions, supported on nowhere-continuousgeneralized connections.

On the Ashtekar-Lewandowski Measure as a Restriction of the Product One