Abstract
A derivation basis ℬ possesses the density property iff it derives the μ-integrals of the characteristic functions of all μ-measurable sets; that is, iff for any ℳ-set M, the density at x, defined as the limit of μ(Ml(x) · M)/μ(Ml(x)), exists and equals c M (x) (characteristic function of M at x) μ*-almost everywhere on E.
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© 1970 Springer-Verlag Berlin Heidelberg
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Hayes, C.A., Pauc, C.Y. (1970). The Converse Problem I: Covering Properties Deduced from Derivation Properties of σ-additive Set Functions. 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_4
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DOI: https://doi.org/10.1007/978-3-642-86180-2_4
Publisher Name: Springer, Berlin, Heidelberg
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