Resumen de On the concentration of measure and the L1-norm

Yuri Malykhin, K.S. Ryutin

• We seek a function in an N-dimensional subspace of L1 that attains a half (more generally, a given part) of its L1-norm on a set of least possible measure. We prove that such a measure is asymptotically maximal when the space is spanned by independent standard normal variables. This answers a question of Y. Benyamini, A. Kro´o, A. Pinkus.