Kharazishvili, A. B.
On the Uniqueness of Lebesgue and Borel Measures
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 R n (sphere S n ) and for the standard Borel measure on the same space (sphere), which is the restriction of the Lebesgue measure to the Borel σ –algebra of R n ( 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.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngJournal of Applied Analysisde Gruyterhttp://www.deepdyve.com/lp/de-gruyter/on-the-uniqueness-of-lebesgue-and-borel-measures-PsGVVdJR9o