Author | Hayes, Charles A. author |
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Title | Derivation and Martingales [electronic resource] / by Charles A. Hayes, Christian Y. Pauc |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1970 |
Connect to | http://dx.doi.org/10.1007/978-3-642-86180-2 |
Descript | VIII, 206 p. 1 illus. online resource |
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. Morseโs 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 -- 1ยฐ. Derivation of vector-valued integrals -- 2ยฐ. Functional derivatives -- 3ยฐ. Topologies generated by measures -- 4ยฐ. Vitaliโs theorem for invariant measures -- 5ยฐ. Global derivatives in locally compact topological groups. -- 6ยฐ. Submartingales with decreasing stochastic bases -- 7ยฐ. Vector-valued martingales and derivation -- 9ยฐ. Derivation of measures