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Important characteristics of the loop approach to quantum gravity are aspecific choice of the algebra A of observables and of a representation of A ona measure space over the space of generalized connections. This representationis singled out by its elegance and diffeomorphism covariance.  Recently, in the context of the quest for semiclassical states, states of thetheory in which the quantum gravitational field is close to some classicalgeometry, it was realized that it might also be worthwhile to study differentrepresentations of the algebra A of observables.  The content of the present note is the observation that under some mildassumptions, the mathematical structure of representations of A can be analyzedrather effortlessly, to a certain extent: Each representation can be labeled bysets of functions and measures on the space of (generalized) connections thatfulfill certain conditions.  These considerations are however mostly of mathematical nature. Theirphysical content remains to be clarified, and physically interesting examplesare yet to be constructed.Comment: LaTeX, 14 pages, no figures. v2: corrected a minor issue with the  mathematical reasoning, updated references; article is now identical to  published versio

Some results concerning the representation theory of the algebra underlying loop quantum gravity