On Vershik's standardness criterion and Tsirelson's notion of cosiness.

Michel Emery (1) , Walter Schachermayer

1 IRMA - Institut de Recherche Mathématique Avancée

"Besides exposing Vershik's theory of standard filtrations and his theorem on lacunary isomorphism, we show that standardness is equivalent to a variant (called I-cosiness) of Tsirelson's notion of cosiness; we show that I-cosiness is strictly stronger than another variant used in earlier works. We also answer a question of von Weizs/"acker on germ sigma-fields. "

Mots clés: filtration; germ sigma-field; "filtration; standard filtration; cosy filtration; germ sigma-field"

Domaines: Probabilités [math.PR]

Michel Emery, Walter Schachermayer. On Vershik's standardness criterion and Tsirelson's notion of cosiness.. 2000. ⟨hal-00129657⟩