Abstract
Let X be a compact metric space, le μ be a non-negative normalized Borel measure on X and let f be a measurable bounded real-valued function defined on X such that f is μ-almost everywhere continuous and different from zero. It is proved that a sequence (x n ), n=1,2, ... of points in X is μ-uniformly distributed if and only if for every Borel set E⊆X with μ(Bd(E))=0 we have {Mathematical expression} where 1 E denotes the characteristic function of E and bdE the boundary of E. Furthermore some quantitative aspects and generalizations of this theorem are discussed.
Original language | English |
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Pages (from-to) | 332-342 |
Number of pages | 11 |
Journal | Rendiconti del Circolo Matematico di Palermo |
Volume | 36 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 May 1987 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)