Normal Numbers from Steinhaus’ Viewpoint

Abstract

Abstract. In this paper we recall a non-standard construction of the Borel sigma-algebraB in [0, 1] and construct a family of measures (in particular, Lebesgue measure) in B by a completely non-topological method. This approach, that goes back to Steinhaus, in 1923, is now used to introduce natural generalizations of the concept of normal numbers and… (More)

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