Abstract
It is proved that the partial sums of a series in the Franklin system with numbers 2μ, μ ∈ ℕ, cannot approach +∞ on a set of positive measure. In particular, a Franklin series cannot converge to +∞ on a set of positive measure.
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Funding
This work was supported by the State Committee on Science of the Ministry of Education and Science of the Republic of Armenia (grant no. 18T-1A074).
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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 3, pp. 341–349.
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Gevorkyan, G.G. On the Convergence of Franklin Series to +∞. Math Notes 106, 334–341 (2019). https://doi.org/10.1134/S0001434619090037
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DOI: https://doi.org/10.1134/S0001434619090037