  We prove a version of Onsager's conjecture on the conservation of energy for
the incompressible Euler equations in the context of statistical solutions, as
introduced recently by Fjordholm et al. As a byproduct, we also obtain a new
proof for the conservative direction of Onsager's conjecture for weak
solutions. Dedicated to Edriss S. Titi on the occasion of his 60th birthday.
