Journal of Applied Analysis EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 3, No. 1, pp. 49-66 (2003)

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On the uniqueness of Lebesgue and Borel measures

A.B. Kharazishvili

Institute of Applied Mathematics
University of Tbilisi
University street 2
380043 Tbilisi 43
Republic of Georgia

Abstract: We consider the uniqueness property for various invariant measures. Primarily, we discuss this property for the standard Lebesgue measure on the $n$-dimensional Euclidean space ${\bold R}^n$ (sphere ${\bold S}^n$) and for the standard Borel measure on the same space (sphere), which is the restriction of the Lebesgue measure to the Borel $\sigma$-algebra of ${\bold R}^n$ (${\bold S}^n$). The main goal of the paper is to show an application of the well known theorems of Ulam and Ershov to the uniqueness property of Lebesgue and Borel measures.

Keywords: Invariant measure, quasiinvariant measure, uniqueness property, real-valued measurable cardinal, measure extension theorem

Classification (MSC2000): 28A05, 28D05

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Electronic version published on: 12 Jun 2003. This page was last modified: 12 Jun 2003.

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