Good afternoon,
I'm typing in $\LaTeX$ a formularium and a compendium of useful probability theorems, corolaries and commonly-used approaches to many topics in preparation to an important exam at my university. Right now I'm working onto the convergence section.
I know that:
Convergence in probability problems often can be solved by applying Chebyshev's inequality and Khintichine's Law of Large Numbers.
Almost-surely convergence problems often can be solved by applying Borel-Cantelli's Lemmas and Kolmogorov's Law of Large Numbers.
Slutsky's theorem is also nice if $X_{n} \xrightarrow[]{} X$ and $Y_{n} \xrightarrow[]{} c$, where $c$ is a constant, and you are working with their product/sum.
I know that every single exercise has it's particularities and "sideboard" procedures, but I'd like to know if there are other theorems/results that are majorly used in those kind of problems. I would be very thankful.