Derivation and Martingales

In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property...

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Main Authors: Hayes, Charles A., Pauc, C.Y. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1970, 1970
Edition:1st ed. 1970
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I Pointwise Derivation
  • I: Derivation Bases
  • II: Derivation Theorems for ?-additive Set Functions under Assumptions of the Vitali Type
  • III: The Converse Problem I: Covering Properties Deduced from Derivation Properties of ?-additive Set Functions
  • IV: Halo Assumptions in Derivation Theory. Converse Problem II
  • V: The Interval Basis. The Theorem of Jessen-Marcin-Kiewicz-Zygmund
  • VI: A. P. Morse’s Blankets
  • II Martingales and Cell Functions
  • I: Theory without an Intervening Measure
  • II: Theory in a Measure Space without Vitali Conditions
  • III: Theory in a Measure Space with Vitali Conditions
  • IV: Applications
  • Complements
  • 1°. Derivation of vector-valued integrals
  • 2°. Functional derivatives
  • 3°. Topologies generated by measures
  • 4°. Vitali’s theorem for invariant measures
  • 5°. Global derivatives in locally compact topological groups.
  • 6°. Submartingales with decreasing stochastic bases
  • 7°. Vector-valued martingales and derivation
  • 9°. Derivation of measures