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Simple topological measures and a lifting problem. (English) Zbl 1155.28002

A certain lifting conjecture is stated and proved in the case of a torus. From this result a connected dense subset of the space of intrinsic simple topological measures on the torus is constructed, consisting of push forwards of compactly supported generalized point-measures on the universal covering space. Combining this result with an observation of Ø. Johansen and A. B. Rustad [Fundam. Math. 177, No. 1, 19–43 (2003; Zbl 1077.28013)], the author concludes that the space of simple topological measures on a torus is connected.

MSC:

28A25 Integration with respect to measures and other set functions
28A51 Lifting theory

Citations:

Zbl 1077.28013
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