  We study the structure of families of well approximable elements of tensor
products of Banach spaces including analogs of the classical quasianalytic
classes in the sense of Bernstein and Beurling. As in the case of quasianalytic
functions, we prove for members of these families variants of the Mazurkiewicz
and Markushevich theorems and in some particular cases, if such elements are
Banach-valued continuous maps on a compact metric space, estimate massivity of
their graphs and level sets.
