The author proves a strong law of large numbers for the position of a tagged particle in a stationary simple exclusion process, which verifies a conjecture of T. M. Liggett [Interacting particle systems. (1985; Zbl 0559.60078)].
For this purpose, the process relative to the tagged particle is studied. It is shown, that the Bernoulli measures conditioned on the existence of a particle at the origin, are extremal invariant for this process.