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The following inequalities are proved: where V (A), V (B) stand for the volumes of convex bodies A and B in R n (n ≥ 2), S(A, B) denotes the area of the surface of the body A relative to the body B, q is the capacity factor of the body B with respect to the body A, A i = A −ti (B) = A/(t i B) is the inner body parallel to the body A with respect to the body B at a distance t i , 0 = t 0 < t 1 < . . T 0 g(t)df (t) is the Riemann-Stieltjes integral of the function g(t) by the function f (t), anddoi:10.15407/mag10.03.309 fatcat:4c4wqoudcfbplgru33ltaqrdp4