''p'' conditional expectation respect sub algebra sub ''t'' sub ''t'' invariant sets linear projector ''e sub sub '' norm banach space ''l sup p sup '' ''x'' '' '' onto closed subspace ''l sup p sup '' ''x'' sub ''t'' sub '' '' latter may also characterized space ''t'' invariant ''l sup p sup '' functions ''x'' ergodic means linear operators ''l sup p sup '' ''x'' '' '' also unit operator norm simple consequence birkhoff khinchin theorem converge projector ''e sub sub '' strong operator topology ''l sup p sup '' ''p'' weak
Formal science Mathematics Pure mathematics Probability theory Ergodic theory