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We study full implementation with evidence in an environment with bounded
utilities. We show that a social choice function is Nash implementable in a
direct revelation mechanism if and only if it satisfies the measurability
condition proposed by <cite>BL2012</cite>. Building on a novel classification
of lies according to their refutability with evidence, the mechanism requires
only two agents, accounts for mixed-strategy equilibria and accommodates
evidentiary costs. While monetary transfers are used, they are off the
equilibrium and can be balanced with three or more agents. In a richer model of
evidence due to <cite>KT2012</cite>, we establish pure-strategy implementation
with two or more agents in a direct revelation mechanism. We also obtain a
necessary and sufficient condition on the evidence structure for
renegotiation-proof bilateral contracts, based on the classification of lies.
