  We present a generalization of the ETH conjecture. Using this generalization
we are able to derive the fact that an arbitrary eigenstate of a general many
body system may be used to represent microcanonical ensemble in any many body
experiment that involves only local operators and projectors onto eigenstates
of the system Hamiltonian. In particular we extend the ETH to include some
non-local operators. We present a derivation of this conjecture in the case of
a many body model whose Hamiltonian is composed of two parts: an integrable
Hamiltonian and a small but finite Gaussian perturbation.
