Pippenger ([Pip77]) showed the existence of (6m; 4m; 3m; 6)-concentrator for each
positive integer m using a probabilistic method. We generalize his approach and prove existence
of (6m; 4m; 3m; 5:05)-concentrator (which is no longer regular, but has fewer edges). We apply
this result to improve the constant of approximation of almost additive set functions by additive
set functions from 44:5 (established by Kalton and Roberts in [KR83]) to 39. We show a more
direct connection of the latter problem to the Whitney type estimate for approximation of
continuous functions on a cube in Rd by linear functions, and improve the estimate of this
Whitney constant from 802 (proved by Brudnyi and Kalton in [BK00]) to 73.
