Probability space associated with a compact group

Question

Is the probability space associated with a compact group with Haar probability always a standard probability space? I recall seeing somewhere the fact that if the topology generating the Borel sigma algebra is not metrizable then the probability space is not standard, or something along these lines. If so then any non-metrizable compact group would show the answer to the above question to be negative, but I am unable to find any firm reference for the above fact. Any help with answering the above question would be much appreciated.