ON LIMIT THEOREMS IN -ALGEBRAS
Abstract: In the present paper, we study bundle convergence in - algebra and prove certain
ergodic theorems with respect to such convergence. Moreover, conditional expectations of
reversible -algebras are considered. Using such expectations, the convergence of
supermartingales is established.
2000 AMS Mathematics Subject Classification: Primary: 46L50, 46L55, 46L53;
Secondary: 47A35, 35A99.
Keywords and phrases: Bundle convergence, Jordan algebra, ergodic theorems,
conditional expectation, enveloping algebra.