Let {(Xi,Yi)}i=1∞ be a |DMS with common pmfpXY on X×Y. Given δ>0 and integer n≥1, the jointly typical set Aδ(n) (or jointly δ -typical set) with respect to the source is Aδ(n)={(xn,yn)∈Xn×Yn:−n1log2(pXn(xn))−H(X)≤δ,−n1log2(pYn(yn))−H(Y)≤δ,−n1log2(pXnYn(xn,yn))−H(X,Y)≤δ}
For a DMS{(Xi,Yi)}i=1∞ with pmfpXY on X×Y, then the joint typical setAδ(n) defined with respect to sourcepXY satisfies: 1. PXnYn(Aδ(n))=P((Xn,Yn)∈Aδ(n))>1−δ for n sufficiently large 2. ∣Aδ(n)∣≤2n(H(X,Y)+δ) 3. ∣Aδ(n)∣≥(1−δ)2n(H(X,Y)−δ) for n sufficiently large