Stability of homogeneity almost everywhere

Stability of homogeneity almost everywhere

We consider approximately h-homogeneous mappings almost everywhere, that is functions F such that the difference F(ax) - h(a)F(x) is in some sense bounded almost everywhere in a product space. We will prove, under some assumptions, that then either we have some kind of boundedness of h and F, or the...

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Veröffentlicht in:Acta mathematica Hungarica 2007-11, Vol.117 (3), p.219-229
1. Verfasser: Jablonski, W
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description We consider approximately h-homogeneous mappings almost everywhere, that is functions F such that the difference F(ax) - h(a)F(x) is in some sense bounded almost everywhere in a product space. We will prove, under some assumptions, that then either we have some kind of boundedness of h and F, or there exist a homomorphism [Equation] and a [Equation]-homogeneous function [Equation], which are almost everywhere equal to h and F, respectively. From this result we derive the superstability effect for the multiplicativity almost everywhere.
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