Abstract
The paper deals with approximations of a functionf of space Lp[0, 1] by rational functions in the metric of this same space (0<p≤∞). It is shown that sufficiently rapid decrease as n→∞ of the least deviations Rn(f, p) of functionf of rational functions of degree no higher than n is evidence of the presence inf of derivatives and differentials of a definite order if differentiation is understood as differentiation in the metric of space Lq[0, 1], with 0<q<q(p), where q(p) depends on p and on the order of differerentiation, q(p)<p.
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