ON METRIC SPACE VALUED FUNCTIONS OF BOUNDED ESSENTIAL VARIATION
Journal Title: Проблемы анализа-Issues of Analysis - Year 2005, Vol 12, Issue
Abstract
Let ∅≠T ⊂ R and let X be a metric space. For an ideal J ⊂ P(T) and a function f:T-> X, we define the essential variation V^J ess(f, T) as the in mum of all variations V (g; T) where g:T-> X, g = f on T\E, and E in J. We show that if X is complete then the essential variation of f is equal to inf{V (f; T\E) : E ∈ J}. This extends former theorems of that type. We list some consequences that are analogues to the recent results by Chistyakov. Some examples of di erent kinds of essential variation are also investigated.
Authors and Affiliations
M. BALCERZAK
Keywords
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