Construction of normal numbers with respect to Generalized Lüroth Series from equidistributed sequences

Generalized Lüroth series generalize $b$-adic representations as well as Lüroth series. Almost all real numbers are normal, but it is not easy to construct one. In this paper, a new construction of normal numbers with respect to Generalized Lüroth Series (including those with an infinite digit set) is given. Our method concatenates the beginnings of the expansions of an arbitrary equidistributed sequence.

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