 This argument is problematic for at least two reasons. First, from the fact that measurements take some time it does not follow that what is actually measured are time averages. For instance, it could be the case that the value provided to us by the measurement device is simply the value assumed by at the last moment of the measurement, irrespective of what the previous values of were (e.g. it’s simply the last pointer reading registered). So we would need an argument for the conclusion that measurements indeed produce time averages. Second, even if we take for granted that measurements do produce finite time averages, equating these averages with infinite time averages is problematic. Even if the duration of the measurement is long by experimental standards (which need not be the case), finite and infinite averages may assume very different values. That is not to say that they necessarily have to be different; they could coincide. But whether or not they do is an empirical question, which depends on the specifics of the system under investigation. So care is needed when replacing finite with infinite time averages, and one cannot identify them without further argument. 