Geodesic
The representations of functions by orthogonal series possessing martingale properties
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 673-680.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathscr F_\infty$ be the minimal $\sigma$-algebra generated by the orthogonal system $\{\varphi_n(x)\}$, defined on the space $(X,S,\mu)$ of finite measure. For a certain class of orthonormal systems one proves that for any $\mathscr F_\infty$-measurable function $f(x)$, which is finite almost everywhere, there exists a series $\sum_{n=1}^\infty a_n\varphi_n(x)$ which converges absolutely to $f(x)$ almost everywhere. This result represents an extension of a theorem by R. Gundy on the representation of functions by orthogonal series possessing martingale properties. 
@article{MZM_1976_19_5_a1,
     author = {R. S. Davtyan},
     title = {The representations of functions by orthogonal series possessing martingale properties},
     journal = {Matemati\v{c}eskie zametki},
     pages = {673--680},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a1/}
}
TY  - JOUR
AU  - R. S. Davtyan
TI  - The representations of functions by orthogonal series possessing martingale properties
JO  - Matematičeskie zametki
PY  - 1976
SP  - 673
EP  - 680
VL  - 19
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a1/
LA  - ru
ID  - MZM_1976_19_5_a1
ER  - 
%0 Journal Article
%A R. S. Davtyan
%T The representations of functions by orthogonal series possessing martingale properties
%J Matematičeskie zametki
%D 1976
%P 673-680
%V 19
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a1/
%G ru
%F MZM_1976_19_5_a1
R. S. Davtyan. The representations of functions by orthogonal series possessing martingale properties. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 673-680. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a1/