On Weak Compactness in Spaces of Measures

  title={On Weak Compactness in Spaces of Measures},
  author={Xiaodong Zhang},
  journal={Journal of Functional Analysis},
Abstract It is proved that a weak* compact subsetAof scalar measures on aσ-algebra is weakly compact if and only if there exists a nonnegative scalar measureλsuch that each measure inAisλ-continuous (such a measureλis called a control measure forA). This result is then used to obtain a very general form of the Vitali–Hahn–Saks Theorem on finitely additive vector measures. Finally, it is proved that a weak* compact subsetAof regular Borel measures on anF-space is weakly compact if and only if… 


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