On the existence of a measurable function with given values of the best approximations in $L_0$ - Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
In the space of convergence in measure, we study the Bernstein problem of existence of a function with given values of the best approximations by a system of finite-dimensional subspaces strictly imbedded in one another.