Tag Archives: SLLN

Marcinkiewicz-Zygmund’s SLLN

First, we present well-known Khintchine-Kolmogorov Theorem. Theorem (Khintchine-Kolmogorov). Let be independent random variables with finite expectation. If , then converges a.e. Now we present the Marcinkiewicz-Zygmund theorem which is our object of this article. Theorem (Marcinkiewicz-Zygmund Theorem). Suppose that are i.i.d with for some . Then     where     Proof. Set    … Read More »