Weak law of large numbers

The Weak Law of Large Numbers (WLLN) says: if $X_{1}, X_{2}, \dots$ are independent and identically distributed (i.i.d.) with finite expectation $μ$ , then

\frac{1}{n} \sum_{k = 1}^{n} X_{k} \to_{n \to \infty}^{P} μ .

So:

Independence + identical distribution (and finite mean) $\Rightarrow$ LLN holds.
But the converse is not true.