Geodesic
A generalization of the Riesz--Fischer theorem
Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 365-372.

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An analog is established, in a certain sense, of the Riesz–Fischer theorem for the space $L^p$, $p\geqslant1$, and a corollary derived. 
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     author = {G. A. Fomin},
     title = {A generalization of the {Riesz--Fischer} theorem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {365--372},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a2/}
}
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G. A. Fomin. A generalization of the Riesz--Fischer theorem. Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 365-372. http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a2/