On a method for random graphs (Q1078580)

For a random graph of order n it might hold that events \(A_{ni}\) and \(B_{ni}\) satisfy \(P(A_{ni})>0\), \(P(B_{ni}| A_{ni})\to 1\), \(P(U_ iA_{ni})\to 1\) and we would like to infer that \(P(U_ iB_{ni})\to 1\) as \(n\to \infty\). A sufficient condition and several illustrations are given.