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.


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    $\begingroup$ It's stronger because it implies the weaker and is harder to prove, I guess. $\endgroup$ – peter.petrov Jun 8 '15 at 22:12
  • $\begingroup$ ok, I seek for any proof or any theory show this mathematical reason $\endgroup$ – zeraoulia rafik Jun 8 '15 at 22:13

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.


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