There are estimated the rates of approximation of 
function $\widetilde{f}$, conjugated to the Lebesgue 
integrable function $f$ , by the Ces{\`{a}}ro and 
Abel-Poisson means of conjugate Fourier series. 
As a measure of such approximation the characteristics 
constructed on the base of definition of the points of 
differentiation of the indefinite Lebesgue integral are used.