Abstract
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 A ⊂ R. 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.
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© 1970 Springer-Verlag Berlin Heidelberg
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Hayes, C.A., Pauc, C.Y. (1970). A. P. Morse’s Blankets. In: Derivation and Martingales. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 49. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86180-2_7
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DOI: https://doi.org/10.1007/978-3-642-86180-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-86182-6
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