A decomposition theorem for numbers in which the summands have prescribed normality properties (Q1080467)

The paper generalizes and refines previous work of the authors [J. Lond. Math. Soc., II. Ser. 32, 12--18 (1985; Zbl 0574.10051)]. Typical results may be described as follows: let \(A, B\) be multiplicatively independent subsets of \(\mathbb Z\setminus \{1\}\). There is a set \(M(w)\) which has full measure with respect to a Riesz product measure \(dq(w)\) such hat every \(x\in M(w)\) is normal to every base of \(A\) but is non-normal to every base of \(B\). Almost every real number can be expressed as a sum \(y=x_1+x_5\), \(x_1\in M(1)\), \(x_5\in M(5)\).