Abstract:
We show that if the partial sums $S_{n_i}(x)=\sum_{k=0}^{n_i}a_kf_k(x)$ of a Franklin series $\sum_{k=0}^{\infty}a_kf_k(x)$, where $\sup_i{n_i}/(n_{i-1})<\infty$, converge in measure to a bounded function $f$ and $\sup_i|S_{n_i}(x)|<\infty$ for $ x\not\in B$, where $B$ is some countable set, then this series is the Fourier-Franklin series of $f$.
Bibliography: 24 titles.
Keywords:Franklin system, Franklin series, uniqueness theorem, Fourier-Franklin series.
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