Questions tagged [monotone-class-theorem]

I've been presented with a definition of monotone classes that I was unfamiliar with : a subset of the power set containing the entire space, closed under countable increasing union and difference between two ordered subsets. I would have thought…

Give an example of a monotone class $\mathcal{G}$ on $\mathbb{R}$ that satisfies: (a) \mathbb{R} belongs to $\mathcal{G},$ and (b)if $A \in \mathcal{G} $ then its complement $A^c$ is in $\mathcal{G},$ but it is not a $\sigma-$algebra. Here is my…

Using the Monotonic Sequence Theorem prove that the following sequences are convergent. () =Σ 1/(+) () 1=1, +1=/√(2+1) , ∈ℤ+