Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 1, pp. 154-157
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I. V. Pavlov. A counterexample to the hypothesis on the $H^\infty$ to be dense in the space BMO. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 1, pp. 154-157. http://geodesic.mathdoc.fr/item/TVP_1980_25_1_a14/
@article{TVP_1980_25_1_a14,
author = {I. V. Pavlov},
title = {A counterexample to the hypothesis on the $H^\infty$ to be dense in the space {BMO}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {154--157},
year = {1980},
volume = {25},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_1_a14/}
}
TY - JOUR
AU - I. V. Pavlov
TI - A counterexample to the hypothesis on the $H^\infty$ to be dense in the space BMO
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1980
SP - 154
EP - 157
VL - 25
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%T A counterexample to the hypothesis on the $H^\infty$ to be dense in the space BMO
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1980
%P 154-157
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%U http://geodesic.mathdoc.fr/item/TVP_1980_25_1_a14/
%G ru
%F TVP_1980_25_1_a14
In the probability space $(\Omega,\mathscr F,\mathbf P)$ we consider a discrete increasing family of $\sigma$-fields $(\mathscr F_n)$ satisfying special conditions. By means of the norm (which is equivalent to that of the space BMO of martingales) we obtain an example of a martingale which belongs to BMO but cannot be approximated (in the BMO-norm) by elements of $H^\infty$.
