(Kolmogorov zero-or-one law). For an
independent process, each remote event has probability zero or one.
(Preservation of stationary
measure) For a stationary independent process and any
is the set
moved by one position to the right in the coordinate representation. But by
stationarity and independence the same measure is assigned to all positions.
(Hewitt and Savage zero-or-one
law) For a stationary independent process, each permutable set has probability
zero or one.