Simple topological measures and a lifting problem

Volume 200 / 2008

Finn F. Knudsen Fundamenta Mathematicae 200 (2008), 201-241 MSC: Primary 28A25; Secondary 28A51. DOI: 10.4064/fm200-3-1


We state a certain lifting conjecture and prove it in the case of a torus. From this result we are able to construct a connected dense subset of the space of intrinsic simple topological measures on the torus, consisting of push forwards of compactly supported generalized point-measures on the universal covering space. Combining this result with an observation of Johansen and Rustad, we conclude that the space of simple topological measures on a torus is connected.


  • Finn F. KnudsenDepartment of Mathematical Sciences
    Norwegian University of Science and Technology
    NO-7491 Trondheim, Norway

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