For a DMS $\{X_i\}_{i=1}^\infty$ with pmf $p_X$ on $\mathcal{X}$ and entropy $H(X)$, given integer $n\ge 1$ and $\epsilon>0$, the typical set $A_\epsilon^{(n)}$ with respect to the source is $$\begin{align*} A_\epsilon^{(n)}&=\left\{a^{n}\in X^{n}:\left|-\frac{1}{n}\log_2(p_{X^{n}}(a^{n}))-H(X)\right|\le\epsilon\right\}\\\\ &=\left\{a^{n}\in X^{n}:2^{-n(H(X)+\epsilon)}\le p_{X^{n}}(a^{n})\le2^{-n(H(X)-\epsilon)}\right\} \end{align*}$$ or the typical set is the set of all n-tuples $a^n=(a_1,\cdots,a_n)$ drawn iid from $\mathcal{X}$ according to $p_X$ whose probability is roughly $2^{-nH(X)}$; or whose “apparent entropy” is within the “true entropy” $H(X)$.