Pettis mean convergence of vector-valued asymptotic martingales
β Scribed by J. J. Uhl
- Publisher
- Springer
- Year
- 1977
- Tongue
- English
- Weight
- 234 KB
- Volume
- 37
- Category
- Article
- ISSN
- 1432-2064
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Given any Banach space X, let L: denote the Banach space of all measurable functions f : [0, 11 + X for which llfllz:=( Ilf(t)ll'dt)l'z is finite. We show that X is a UMD-space (see [l]) if and only if lim [ I f -SJj)llZ = O for all EL.:, n where n-1 SnCnl= C (h wi>wi i = o is the n-th partial sum
The purpose of this paper is to prove the convergence theorems of set-valued and fuzzy-valued martingales in Kuratowski-Mosco sense without assuming that their values are compact or of compact level sets.
We study weighted inequalities for vector valued extensions of the conditioned square function operator and of the maximal operators of matrix type in the case of regular martingales. As applications we obtain weighted inequalities for vectorvalued extensions of the HardyαLittlewood maximal operator