Hi, I keep seeing this come up(adsbygoogle = window.adsbygoogle || []).push({});

A1 ⊇ A2 ⊇ A3 .... is an infinite decreasing sequence of events. Prove from first principles

that

P(intersection of Ai from i=1 to infinity) = Lim P(An) as n--> infinity

All i can think of is that since each is a subset of the preceding, then A1 ∩ A2...∩An = An

So clearly P(A1 ∩ A2...∩An) = P(An) and thus the same for limits.

I think this is too simplistic though, is it or isnt it ?

Thanks a lot

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limit of the intersection of events

Loading...

Similar Threads for Limit intersection events |
---|

I Probability of equally likely events |

A What exactly is a "rare event"? (Poisson point process) |

A Averaging over the upper sum limit of a discrete function |

I Probability of an event in n tries |

**Physics Forums | Science Articles, Homework Help, Discussion**