manuscripta mathematica

, Volume 39, Issue 2–3, pp 271–276 | Cite as

Boundedness properties for functional inequalities

  • Wolfgang Sander


It is well known, that a subadditive or convex function f: IRn → IR is bounded above on each compact subset of IRn, whenever f is bounded above on a set of positive Lebesgue measure. Considering a more general inequality of the type f[F(x,y)] ⩽ g(x) + h(y), we prove in this note an analogous result, replacing the measure theoretical conditions by appropriate topological conditions.


Open Subset Convex Function Compact Subset Analogous Result Analogous Manner 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Wolfgang Sander
    • 1
  1. 1.Institut C für MathematikTechnische Universität BraunschweigBraunschweigGermany

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