Derivation and Martingales

Derivation and Martingales Description

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.