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  • 1 Department of Mathematics Temple University 19122 Philadelphia Pennsylvania U.S.A.
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Summary After an introductory section on problems and results concerning expansions of real numbers by given algorithms, I shall prove several new theorems for β-expansions with non-integral β. For the special case βn - βn−1=1, I shall re-obtain and sharpen known results by a neat approach, reducing the usual questions to sums of independent and identically distributed random variables.