Abstract
We establish, in particular, that, for certain natural concepts of convergence, there are no bases in the corresponding spaces of measureable functions.
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D. E. Men'shov, “Sur la représentation des fonctions mesurables par des series trigonométriques,” Mat. Sb.,9, 667–692 (1941).
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Translated from Matematicheski Zametki, Vol. 5, No. 1, pp. 3–12, January, 1969.
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Talalyan, A.A. On the existence of null series in certain systems of functions. Mathematical Notes of the Academy of Sciences of the USSR 5, 3–9 (1969). https://doi.org/10.1007/BF01098707
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DOI: https://doi.org/10.1007/BF01098707