The oscillation of separately locally Lipschitz functions

  • V.H. Herasymchuk Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
  • O.V. Maslyuchenko Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
Keywords: oscillation, locally Lipschitz function, separately locally Lipschitz function, $C\mathcal{L}$-function
Published online: 2011-06-30

Abstract


We prove that a function which defined on the product of two metric Baire spaces is the oscillation of some separately locally Lipschitz function if and only if it is an upper semi-continuous non-negative function which has a crosswise nowhere dense closure of its support.

How to Cite
(1)
Herasymchuk V., Maslyuchenko O. The Oscillation of Separately Locally Lipschitz Functions. Carpathian Math. Publ. 2011, 3 (1), 22–33.