Let $(X_i)_{i \in \Bbb N}$ be a sequence of independent RV's with zero means $\Bbb E[X_i]=0$ and let $(b_i)_{i \in \Bbb N}$ be an increasing sequence of positive numbers satisfying $\sum_i \Bbb E[X_i^2]/b_i^2 < \infty$.
Set $S_n:= \sum_{k=1}^n X_k$.
Question 1: How to see that $\varinjlim_{n \to ...
Here are two questions about the limits of an integral, which are essentially duplicates of each other: The older question (from 2015) is more generic with parameters a and b, the newer question (from 2017) is more specific, but has five different answers.
Any suggestion which one to choose as the duplicate target?
(I am also asking because I have another solution in mind, and want do add that only to one of the two questions.)
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@SineoftheTime I am not sure if there is some connection between those questions, but the second one is now closed as a duplicate. I voted to close the first one (missing context) because it is unclear which tools can be used.
