Infinitely Often

1. Feb 9, 2005

jetoso

Let (R, B, P) be a probability space, where P is some given probability measure. For n = 2, 3, … , define En = (an, bn) where

an = min { 1/n , (-1)^n + 1/n } and bn = max { 1/n , (-1)^n + 1/n }

Write the events {En i.o.} and {En almost always}.
i.o. = infinitely often

Need help with this... it means that {En i.o.} = {(-1)^n} since its going to be in the limsup, and {En almost always} = {1/n}?

Last edited: Feb 9, 2005
2. Feb 10, 2005

Hurkyl

Staff Emeritus
Do not multiple post.