The criterion of the best approximant for the multivariable functions in the space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$

The questions of the characterization of the best approximant for the multivariable functions in the space with mixed integral metric were considered in this article. The criterion of the best approximant in space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$ is obtained.