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I have seen different types of convergence among random variables

  1. Almost sure.
  2. In mean.
  3. In probability.
  4. In distribution.

What are the differences between them, I'm looking for a more intuitive answer. In addition, every type of convergence has a particular mode to check the convergence. I realized for example, that to check convergence in mean and probability you have to use a lot of inequalities. Is there advices to check every convergence?

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