The oscillation of separately locally Lipschitz functions

The oscillation of separately locally Lipschitz functions

We prove that a function which dened 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 semicontinuous non-negative function which has a crosswise nowhere dense closure of its support.

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Veröffentlicht in:Karpats'kì matematinì publìkacìï 2013-01, Vol.3 (1), p.22-33
Hauptverfasser: V. H. Herasymchuk, O. V. Maslyuchenko
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove that a function which dened 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 semicontinuous non-negative function which has a crosswise nowhere dense closure of its support.
ISSN:2075-9827
2313-0210
DOI:10.15330/cmp.3.1.22-33