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Generalized L\"uroth series generalize $b$-adic representations as well asL\"uroth series. Almost all real numbers are normal, but it is not easy toconstruct one. In this paper, a new construction of normal numbers with respectto Generalized L\"uroth Series (including those with an infinite digit set) isgiven. Our method concatenates the beginnings of the expansions of an arbitraryequidistributed sequence.

Construction of normal numbers with respect to Generalized L\"uroth Series from equidistributed sequences