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We considered the problem of obtaining upper bounds for the mathematicalexpectation of the $q$-norm ($2\leqslant q \leqslant \infty$) of the vectorwhich is uniformly distributed on the unit Euclidean sphere. We finish thepaper with numerical experiments illustrating our results.

mathematical notes/mathematical notes of the academy of sciences of the ussr

On the upper bound for the mathematical expectation of the norm of a  vector uniformly distributed on the sphere and the phenomenon of  concentration of uniform measure on the sphere