Sigma Algebra

[korakardie]

Hi,
Just a really quick question actually. I'm not sure what this notation means, can anyone help?

F_i , i = {1, . . . , n}

I basically have to show that the Intersection of all F_i from 1 to n is the sigma algebra F of Omega.

 

[HallsofIvy]

Hi,
Just a really quick question actually. I'm not sure what this notation means, can anyone help?

F_i , i = {1, . . . , n}

That means that means that you are considering a collection of n objects, labled F_1, F_2, F_3, etc, up to F_n.

I basically have to show that the Intersection of all F_i from 1 to n is the sigma algebra F of Omega.

So those "objects" are sets and you take the intersection of them. You want to show this gives a "sigma algebra". What is a "sigma algebra"?

 

[korakardie]

That means that means that you are considering a collection of n objects, labled F_1, F_2, F_3, etc, up to F_n.

So if i write F_1 = {1}, F_2 = {1,2} ? like this

So those "objects" are sets and you take the intersection of them. You want to show this gives a "sigma algebra". What is a "sigma algebra"?

σ-Algebra,from what i recently learned it like the sets of divided countable set of an uncountable set omega. if that makes sense.
F ⊆ 2^Ω

 

[HallsofIvy]

My point was that, obviously, in order to prove that something is a "sigma algebra" you need to know a precise definition of "sigma algebra" and show that this thing satisfies every detail of that definition.