Abstract
On any uncountable Polish space we construct a sequence of continuous functions $(f_n)$ such that $\sum f_{n}$ is divergent everywhere, but for a typical sign sequence $(\varepsilon_n) \in \{-1, +1\}^{\mathbb{N}}$, the series $\sum \varepsilon_{n} f_{n}$ is convergent in at least one point. This answers a question of S. Konyagin in the negative.
Citation
Tamás Keleti. Tamás Mátrai. "A nowhere convergent series of functions which is somewhere convergent after a typical change of signs.." Real Anal. Exchange 29 (2) 891 - 894, 2003-2004.
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