Kharazishvili, A. B. On the uniqueness of Lebesgue and Borel measures. (English) Zbl 0908.28003 J. Appl. Anal. 3, No. 1, 49-65 (1997). Summary: 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 \(\mathbb{R}^n\) (sphere \(\mathbb{S}^n\)) 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 \(\mathbb{R}^n\) \((\mathbb{S}^n)\). 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. Cited in 1 Document MSC: 28A12 Contents, measures, outer measures, capacities 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets 28D05 Measure-preserving transformations Keywords:invariant measure; quasiinvariant measure; real-valued measurable cardinal; measure extension theorem; uniqueness; Lebesgue measure; Borel measure PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, J. Appl. Anal. 3, No. 1, 49--65 (1997; Zbl 0908.28003) Full Text: DOI EuDML