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Feb 1, 2012 at 21:03 comment added user5810 I expect uniqueness to fail. $\;$ Yes, and for that matter it happens even for a finite-(real-)valued measurable Aleph, since any such measure could be rescaled to be a probability measure.
Feb 1, 2012 at 15:00 comment added Gerald Edgar Your "measurable cardinal" failure even happens if you use the discrete topology in the two factors, right?
Feb 1, 2012 at 15:00 comment added Gerald Edgar (*) says "there exists a unique" ... when if fails, do you expect existence or uniqueness to fail?
Feb 1, 2012 at 4:52 comment added user5810 $\operatorname{Ba}$ stands for Baire (Dudley's definition, en.wikipedia.org/wiki/Baire_set#More_general_definitions) $\;$
Feb 1, 2012 at 4:34 history asked user5810 CC BY-SA 3.0