. "Convergence of a typical martingale (A remark on the Doob theorem)"@en . "414" . "2" . . "0022-247X" . "Zelen\u00FD, Miroslav" . . . "We study convergence behavior of discrete martingales with values in the interval [0,1] from a measure theoretical point of view as well as from a topological one. We show that almost all martingales converge to 0 or 1 almost everywhere. On the other hand, a typical martingale diverges on a comeager set."@en . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "[4DDEAB110668]" . "8895" . . "Spurn\u00FD, Ji\u0159\u00ED" . "2"^^ . "2"^^ . "10.1016/j.jmaa.2014.01.051" . . "Doob theorem; Typical behavior; Martingale"@en . "Journal of Mathematical Analysis and Applications" . . "RIV/00216208:11320/14:10284970" . "We study convergence behavior of discrete martingales with values in the interval [0,1] from a measure theoretical point of view as well as from a topological one. We show that almost all martingales converge to 0 or 1 almost everywhere. On the other hand, a typical martingale diverges on a comeager set." . . "http://dx.doi.org/10.1016/j.jmaa.2014.01.051" . . "I, P(GAP201/12/0290), P(GAP201/12/0436)" . "14"^^ . . . . . "RIV/00216208:11320/14:10284970!RIV15-MSM-11320___" . "Convergence of a typical martingale (A remark on the Doob theorem)" . . "11320" . . "Convergence of a typical martingale (A remark on the Doob theorem)" . "000334651500030" . "Convergence of a typical martingale (A remark on the Doob theorem)"@en . . .