Geodesic
A Martingale Convergence Theorem in Vector Lattices
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 424-432

Voir la notice de l'article provenant de la source Cambridge University Press

The martingale convergence theorem was first proved by Doob (3) who considered a sequence of real-valued random variables. Since various collections of real-valued random variables can be regarded as vector lattices, it seems of interest to prove the martingale convergence theorem in an arbitrary vector lattice. In doing so we use the concept of order convergence that is related to convergence almost everywhere, the type of convergence used in Doob's theorem. 
DeMarr, Ralph. A Martingale Convergence Theorem in Vector Lattices. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 424-432. doi: 10.4153/CJM-1966-045-x
@article{10_4153_CJM_1966_045_x,
     author = {DeMarr, Ralph},
     title = {A {Martingale} {Convergence} {Theorem} in {Vector} {Lattices}},
     journal = {Canadian journal of mathematics},
     pages = {424--432},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-045-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-045-x/}
}
TY  - JOUR
AU  - DeMarr, Ralph
TI  - A Martingale Convergence Theorem in Vector Lattices
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 424
EP  - 432
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-045-x/
DO  - 10.4153/CJM-1966-045-x
ID  - 10_4153_CJM_1966_045_x
ER  - 
%0 Journal Article
%A DeMarr, Ralph
%T A Martingale Convergence Theorem in Vector Lattices
%J Canadian journal of mathematics
%D 1966
%P 424-432
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-045-x/
%R 10.4153/CJM-1966-045-x
%F 10_4153_CJM_1966_045_x

[1] 1. Birkhoff, G., Lattice theory (Providence, R.I., 1948). Google Scholar

[2] 2. Bochner, S., Partial ordering in the theory of martingales, Ann. of Math., 62 (1955), 162–169. Google Scholar

[3] 3. Doob, J. L., Stochastic processes (New York, 1953). Google Scholar

[4] 4. Kantorovich, L. V., Pinsker, A. G., and Vulikh, B. Z., Functional analysis in semi-ordered spaces (Russian) (Moscow-Leningrad, 1950). Google Scholar

[5] 5. Loève, M., Probability theory (Princeton, 1955). Google Scholar

[6] 6. Vulikh, B. Z., Introduction to the theory of semi-ordered spaces (Russian) (Moscow, 1961). Google Scholar

Cité par Sources :