Geodesic
On the existence of null series in certain systems of functions
Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 3-12.

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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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A. A. Talalyan. On the existence of null series in certain systems of functions. Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a0/