Geodesic
On systems of convergence in measure for $l_2$
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 337-340

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In this article it is proved that every system of convergence in measure for $l_2$ can be made orthonormal by correction on a set of arbitrarily small measure. 
@article{MZM_1973_13_3_a0,
     author = {E. M. Nikishin},
     title = {On systems of convergence in measure for $l_2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {337--340},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a0/}
}
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E. M. Nikishin. On systems of convergence in measure for $l_2$. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 337-340. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a0/