3 ms·
All of this is fine for real-valued inputs and outcomes. It's the number of events (coin flips, measurements, etc) that we're restricting to be countable.
by jeffcoat 11y ago
All of this is fine for real-valued inputs and outcomes. It's the number of events (coin flips, measurements, etc) that we're restricting to be countable.
- graycat 11y agoNo, the number of events is necessarily also finite or uncountable. Indeed, it is a nice exercise that there are no countably infinite sigma algebras (extra credit for a solution!). It's just can't take uncountably many events, take their union, and assume that the result is also an event.