A. P. Morse’s Blankets

  • Charles A. Hayes
  • Christian Y. Pauc
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 49)


We now consider some of A. P. Morse’s blankets (I. 3.3). Throughout this chapter R denotes a metric space metrized by δ. At times, R and δ will be specialized. The terms bounded, open, Borel, etc., will be used relative to δ. We denote by δ (A) the δ-diameter of an arbitrary set AR. The spreads of all Morse’s blankets are families of bounded Borel sets. He also introduces a Carathéodory measure function (outer measure) φ, finite on bounded sets [cf. 44, 43]. We may regard our measure μ, defined on the Borel sets and finite on bounded Borel sets, to have been induced by such a function φ, we let μ* denote, as usual, the completion of μ. Since μ* agrees with μ on the bounded Borel subsets of R, we never need to refer explicitly to φ.


Radon Measure Fine Covering Outer Measure Finite Subfamily Transfinite Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • Charles A. Hayes
    • 1
  • Christian Y. Pauc
    • 2
  1. 1.University of CaliforniaDavisUSA
  2. 2.University of NantesNantesFrance

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