Bernoulli Action

A Bernoulli action of a countable discrete group is its shift action on a product probability space with independent coordinates having distribution . For , the action is

It preserves the product measure. For example, the base interval with Lebesgue measure gives an essentially free action of every countable group: each nonidentity element fixes a null set. For this is a two-sided Bernoulli scheme. The fixed price problem compares costs of this action with other essentially free actions.