On two set-systems with restricted cross-intersections

If A1, …, Am; B1, …, Bm are finite sets such that for l ⩾ t ⩾ 0 and any r, s, we have |Ai| ⩽ r, |Bi| ⩽ s and |i ∩ Bi| ⩽ t for 1 ⩽ i ⩽ m and |Ai ∩ Bi| > l for 1 ⩽ i < j ⩽ m, what is the maximum value that m can attain? In this paper we answer this question of Füredi and extend an inequality of Bollobás.im]0658.TIF