Hi !

Now it's the turn of measure theory

I don't understand something I've read...

We have a sequence of sigma-algebras .

And is the smallest sigma-algebra containing every

There's a property one wants to prove for any in

And it is said that

I'm not sure : can we write that ? I think an uncountable union of sigma-algebras is a sigma-algebra, but I still have some doubts. Otherwise, I know I can just say that is generated by the union.Assume we can prove the desired identity for all n and for all .

By the monotone class theorem, the identity holds true for any and all n and all and so on...

Next point, I don't understand how the monotone class theorem acts here... I followed a link in the Wikipedia to transfinite induction. I have an intuition that the explanation has something to do with that, but I'm sorry to say that I didn't understand much in it, or rather how to use it here...

So is anyone able to explain it to me, please ? ^^

Thank you