# Tagged Questions

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### Translating math into words for lim sup complement

I'm self-studying some more theoretical probability theory, and I came across this problem: Show that $\left( \text{lim sup } A_n \right)^c = \text{lim inf } A_n^c$ and give an interpretation when ...
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### Halmos “Measure theory” exercise on limit of sequence of sets

Problem statement. This is an exercise from chapter 1, section 4 (problem 13) from Halmos textbook: If $\{E_n\}$ is a sequence of sets, write $D_1=E_1, D_2=D_1 \triangle E_2, D_3=D_2 \triangle E_3$ ...
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### limsup liminf of sequence of sets

Following up from the discussion here: Liminf and Limsup of a sequence of sets I wanted to confirm my understanding of these concepts with another example. Suppose we have: $a_n>0$, $b_n >1$ ...
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### A problem in Sigma algebra.

How do I conceptualise this expression : Let {$A_n$}$^{n=\infty}_{n=1}$ belong to sigma algebra $A$. Define, $\limsup\{A_{n}\}=\bigcap_{n=1}^{\infty}\{\bigcup_{m=n}^{\infty}A_{n}\}$ and similarly ...