Lemma 5.1. Assuming that:

  • c>0 is such that

    h(xy)c(xh(y)+yh(x))

    for every x,y[0,1]

  • A is a family of sets such that every element (of A) belongs to fewer than p|A| members of A

Then H[AB]>c(1p)(H[A]+H[B]).