  We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices
uniformly in the entire spectrum, in particular near the spectral edges, with a
bound on the fluctuation that is optimal for any observable. This complements
earlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,
Sigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:
2303.11142) that were restricted either to the bulk of the spectrum or to
special observables. As a main ingredient, we prove a new multi-resolvent local
law that optimally accounts for the edge scaling.
