The two perspectives are easily interchangeable, so I don’t think this is a big disagreement. But the argument about extending a distribution seems… awful? I could just as well say that I can extend my event algebra to include some new events which cannot be represented as values of random variables over the original event algebra, “so random variables are less general”.
The two perspectives are easily interchangeable, so I don’t think this is a big disagreement. But the argument about extending a distribution seems… awful? I could just as well say that I can extend my event algebra to include some new events which cannot be represented as values of random variables over the original event algebra, “so random variables are less general”.