Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 845-865

ASYMPTOTIC BEHAVIOUR OF MOMENTS AND LOCAL DIMENSIONS OF MEASURES

Lars Olsen

University of St. Andrews, Department of Mathematics
St. Andrews, Fife KY16 9SS, Scotland; lo 'at' st-and.ac.uk

Abstract. We analyse the asymptotic behaviour of several types of moments of Borel probability measures on R^d. In particular, we prove that the asymptotic behaviour of the moments of a measure is intimately related to the local dimensions of the measure.

2010 Mathematics Subject Classification:

Key words: Moments of measures, local dimension, Rényi dimension.

Reference to this article: L. Olsen: Asymptotic behaviour of moments and local dimensions of measures. Ann. Acad. Sci. Fenn. Math. 41 (2016), 845-865.

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doi:10.5186/aasfm.2016.4156