Abstract:
In this paper it is proved that for each bounded orthonormal system $\{\varphi_n(x)\}$ complete in $L^2[0,1]$ there is a series $\sum_{n=1}^\infty a_n\varphi_n(x)$ having the property that for each measurable function $F(x)$ ($F(x)$ can assume infinite values) the terms of the series $\sum_{n=1}^\infty a_n\varphi_n(x)$ can be rearranged so that the resultant series converges almost everywhere to $F(x)$.
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