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In this paper, order estimates for the Kolmogorov $n$-widths of anintersection of a family of balls in a mixed norm in the space$l^{m,k}_{q,\sigma}$ with $2\le q, \, \sigma <\infty$, $n\le mk/2$ areobtained.

Kolmogorov widths of an intersection of a family of balls in a mixed norm