weak law of large numbers

Let random variables$X_1,X_2,\cdots,X_n$ be $i.i.d.$ and any $E(X_i)=\mu<\infty$. If we put
\[ Y_n=\frac{1}{n}\sum_{i=1}^nX_i \]
then,
\[ P(\lim_{n\rightarrow\infty}Y_n=\mu)=1 \]
It is called strong law of large numbers.

On the other hand, weak law of large numbers has a weaker assertion in which $Y_n$ approches $\mu$ than strong law of large numbers. It says, for any $\epsilon>0$,
\[ P(\lim_{n\rightarrow\infty}|Y_n-\mu|>\epsilon )=0\quad  \]
Weak law of large numbers does not say that $Y_n$ approaches $\mu$ with probability 1.

On mathematical terms, strong law of large numbers is a almost everywhere convergence. Weak law of large numbers is a convergence in probability. Therefore, in the random variables, if strong law of large numbers is true, then weak law of large numbers is true. However the converse is not true.