On the best approximation in the space
In the space of functions summable on the segment, the norm is defined as the maximum of the integral over all possible segments entering the initial segment. In this space I. V. Price obtained necessary and sufficient conditions for best approximation of functions by algebraic polynomials. In this note, this result is transferred to the polynomials in the Chebyshev system. Next, the article considers the approach of the linearly independent system, not forming a Chebyshev system, the primitive conditions were imposed.