The **strong law of large numbers (SLLN)** is usually stated in the following way:

**Theorem:** For such that the ‘s are independent and identically distributed (i.i.d.) with finite mean , as ,

**What if the ‘s are independent but not identically distributed?** Can we say anything in that setting? We can if we add a condition on the sum of the variances of the ‘s. This is sometimes known as **Kolmogorov’s strong law of large numbers** or the **Kolmogorov criterion**.

**Theorem:** Assume that are independent with means and variances such that . Then

References:

- WolframMathWorld. Strong Law of Large Numbers.

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