On concentrators and related approximation constants

@article{Bondarenko2012OnCA,
  title={On concentrators and related approximation constants},
  author={A. Bondarenko and A. Prymak and D. Radchenko},
  journal={Journal of Mathematical Analysis and Applications},
  year={2012},
  volume={402},
  pages={234-241}
}
Abstract Pippenger (1977) [3] showed the existence of ( 6 m , 4 m , 3 m , 6 ) -concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of ( 6 m , 4 m , 3 m , 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 (1983) [2] ) to 39. We show a more… Expand
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