Israel Journal of Mathematics

, Volume 55, Issue 3, pp 350–362 | Cite as

Uniform separation of points and measures and representation by sums of algebras

  • Yaki Sternfeld


LetX andY i, 1 ≦ik, be compact metric spaces, and letρ i:XY i be continuous functions. The familyF={ρ i} i 1/k is said to be ameasure separating family if there exists someλ > 0 such that for every measureμ inC(X)*, ‖μ o ρ i −1 ‖ ≧λμ ‖ holds for some 1 ≦ik.F is auniformly (point) separating family if the above holds for the purely atomic measures inC(X)*. It is known that fork ≦ 2 the two concepts are equivalent. In this note we present examples which show that fork ≧ 3 measure separation is a stronger property than uniform separation of points, and characterize those uniformly separating families which separate measures. These properties and problems are closely related to the following ones: letA 1,A 2, ...,A k be closed subalgebras ofC(X); when isA 1 +A 2 + ... +A k equal to or dense inC(X)?


Separate Measure Strong Property Measure Separation Atomic Measure Disjoint Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Hebrew University 1986

Authors and Affiliations

  • Yaki Sternfeld
    • 1
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael

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