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Feb 26, 2010 at 11:42 comment added Harald Hanche-Olsen It is quite common to identify functions (or stochastic variables, in this case) that are equal a.e. (almost certainly). You are correct that one should consider a quotient, but unless specifically concerned with what happens on sets of measure zero, most practitioners sort of sweeps it under the carpet. It is quite safe so long as you know what you are doing.
Feb 26, 2010 at 8:20 history answered vitp CC BY-SA 2.5