The weak law is easy to prove, but the strong law (which of course implies the weak law, by Egoroff’s theorem) is more subtle.
I'd like to know for which mathematical reason is the strong law stronger than weak law?
Any kind of help is appreciated.
2026-03-29 07:40:26.1774770026
Why is the strong law of large number stronger than weak law?
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The strong law of large numbers establishes almost sure convergence.
The weak law of large numbers establishes convergence in probability.
Almost sure convergence implies convergence in probabilty. That's why the first variant of the law is stronger than the second.