- #1
Appleton
- 91
- 0
If (E[itex]_{n}[/itex])) is either an increasing or decreasing sequence of events, then
lim n[itex]\rightarrow[/itex]∞ P(E[itex]_{n}[/itex]) = P(lim n[itex]\rightarrow[/itex]∞ (E[itex]_{n}[/itex]))
This seems to be saying that the limit as n goes to infinity of the probability of an increasing or decreasing sequence of events is equal to the probability as n goes to infinity of an increasing or decreasing sequence of events. I can't see a significant difference that merits the kind of proofs I see in the textbooks. What is the significance of moving the limit inside the brackets? Clearly I'm missing something. Could someone give me some intuition on this please?
lim n[itex]\rightarrow[/itex]∞ P(E[itex]_{n}[/itex]) = P(lim n[itex]\rightarrow[/itex]∞ (E[itex]_{n}[/itex]))
This seems to be saying that the limit as n goes to infinity of the probability of an increasing or decreasing sequence of events is equal to the probability as n goes to infinity of an increasing or decreasing sequence of events. I can't see a significant difference that merits the kind of proofs I see in the textbooks. What is the significance of moving the limit inside the brackets? Clearly I'm missing something. Could someone give me some intuition on this please?