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manuscripta mathematica

, Volume 18, Issue 1, pp 25–42 | Cite as

Verallgemeinerungen eines Satzes von H. Steinhaus

  • Wolfgang Sander
Article

Abstract

The following result is due to H. Steinhaus [20]: “If A,B⊂R are sets of positive inner Lebesgue measure and if the function f: R x R→R is defined by f(x,y):=x+y (x,yɛR), then the interior of f(A x B) is non void”. In this note there is proved, that the theorem of H. Steinhaus remains valid, if
  1. (1)

    R is replaced by certain topological measure spaces X, Y and a Hausdorff space Z,

     
  2. (2)

    f is a continuous function from an open set T⊂X x Y into Z and satisfies a special local (respectively global) solvability condition in T,

     
  3. (3)

    A⊂X is a set of positive outer measure, B⊂Y contains a set of positive measure and A x B⊂T.

     

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

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

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