Geodesic
Theorems on representation of functions by series
Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1873-1889 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that if a system $\Phi$ of functions is such that each measurable function that is finite almost everywhere can be represented by a $\Phi$-series convergent in measure, then the same is true for measurable functions that can be equal to plus infinity or minus infinity on sets of positive measure. 
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K. S. Kazarian; D. Waterman. Theorems on representation of functions by series. Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1873-1889. http://geodesic.mathdoc.fr/item/SM_2000_191_12_a5/

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