Аннотация:We consider the problem of the rate of approximation of continuous 2π-periodic functions of class WrH[ω]C by trigonometric polynomials of order n on sets of total measure. We prove that when r≥0,ω(δ)δ −1 → ∞ (δ → 0) there exists a function f ε WrH[ω]C such thatf ε WrH[ω]C and for any sequence {tn n=1 ∞ we have almost everywhere on [0, 2π] limn→∞−−−−|f(x)−tn(x)|nrω−1(1/n)>Cx>0,limn→∞−−−−∣∣f˜(x)−tn(x)∣∣nrω−1(1/n)>Cx>0.