Asymptotic distribution of functions on compact homogeneous spaces (Q1117972)

The authors study distribution properties of continuous functions on compact connected homogeneous Riemannian manifolds \(X\) (generalizing known results in the special case \(X=\mathbb{R}^n/\mathbb{Z}^n)\). It is proved that almost all functions are uniformly distributed and almost no functions are well distributed. Similar results are obtained for sequences. The authors also announce a law of iterated logarithm for the discrepancy of functions on compact connected Riemannian manifolds [using results of \textit{W. Philipp}, Mem. Am. Math. Soc. 114 (1971; Zbl 0224.10052)].