Geodesic
On Hilbert subspaces of $l_p$-spaces having full measure
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 3, Tome 55 (1976), pp. 3-14 
B. Diallo. On Hilbert subspaces of $l_p$-spaces having full measure. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 3, Tome 55 (1976), pp. 3-14. http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a0/
@article{ZNSL_1976_55_a0,
     author = {B. Diallo},
     title = {On {Hilbert} subspaces of $l_p$-spaces having full measure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {3--14},
     year = {1976},
     volume = {55},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the space $l_p$, $1\leq p\leq2$, every probabilistic measure is concentated on some Hilbert subspace. In case $p>2$ there exist measures for which no Hilbert subspace has positive measure.