Knudsen, Finn F. Simple topological measures and a lifting problem. (English) Zbl 1155.28002 Fundam. Math. 200, No. 3, 201-241 (2008). 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. Reviewer: Uta Freiberg (Canberra) MSC: 28A25 Integration with respect to measures and other set functions 28A51 Lifting theory Keywords:topological measure; quasi–linear functional; vh–curves; lifting of families of subset; torus Citations:Zbl 1077.28013 PDFBibTeX XMLCite \textit{F. F. Knudsen}, Fundam. Math. 200, No. 3, 201--241 (2008; Zbl 1155.28002) Full Text: DOI