Divergence of interpolation processes on sets of the second category

C([0, 1]) is the space of real continuous functions f(x) on [0, 1] and ω(δ) is a majorant of the modulus of continuity ω(f, δ), satisfying the condition (mathop {overline {lim } }limits_{n to infty } omega (1/n) ln n = infty ) . A solution is given to a problem of S. B. Stechkin: for any matrix (mathfrak{M}) of interpolation points there exists an f(x) ? c([0, 1]), ω (f, δ) = o{ω(δ)} whose Lagrange interpolation process diverges on a set ? of second category on [0, 1].