  Eigenstate thermalization hypothesis (ETH) is discussed. We show that one
common formulation of ETH does not necessarily imply thermalization of an
observable of isolated many body quantum system. To get thermalization one has
to postulate the canonical or microcanonical distribution in the ETH-ansatz.
More generally, any other average can be postulated in the generalized
ETH-ansatz which leads to a corresponding equilibration condition.
