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An eternally inflating universe produces an infinite amount of spatialvolume, so every possible event happens an infinite number of times, and it isimpossible to define probabilities in terms of frequencies. This problem isusually addressed by means of a measure, which regulates the infinities andproduces meaningful predictions. I argue that any measure should obey certaingeneral axioms, but then give a simple toy model in which one can prove that nomeasure obeying the axioms exists. In certain cases of eternal inflation thereare measures that obey the axioms, but all such measures appear to beunacceptable for other reasons. Thus the problem of defining sensibleprobabilities in eternal inflation seems not be solved.

Is there any coherent measure for eternal inflation?