Symmetry properties of average densities and tangent measure distributions of measures on the line

Answering a question by Bedford and Fisher we show that for every Radon measure on the line with positive and finite lower and upper densities the one-sided average densities always agree with one half of the circular average densities at almost every point. We infer this result from a more general formula, which involves the notion of a tangent measure distribution introduced by Bandt and Graf. This formula shows that the tangent measure distributions are Palm distributions and define self-similar random measures in the sense of U. Zähle.

Metadaten
Author:	Peter Mörters
URN:	urn:nbn:de:hbz:386-kluedo-7879
Series (Serial Number):	Preprints (rote Reihe) des Fachbereich Mathematik (292)
Document Type:	Preprint
Language of publication:	English
Year of Completion:	1995
Year of first Publication:	1995
Publishing Institution:	Technische Universität Kaiserslautern
Date of the Publication (Server):	2000/04/03
Tag:	Palm distributions; average densities; geometry of measures; order-two densities; tangent measure distributions
Source:	Adv. Appl. Math.
Faculties / Organisational entities:	Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:	5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):	28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
	28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx]
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G57 Random measures
Licence (German):	Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011