Let n,k and r≥8 be positive integers. Suppose that a family F is contained in (k [n]) satisfies F1∩∩Fr≠0/ for all F1,…,Fr∈F and ∩F∩FF=0/. We prove that there exist εr>0 and nr such that |F| ≤ (r + 1) (k-r n-r-1) + (k-r-1 n-r-1) holds for all n and k, satisfying n>nr and |k - 1/2|<εr.
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机译：令n，k和r≥8为正整数。假设在（k [n]）中包含一个族F，对于所有F1，…，Fr∈F和∩F∩FF= 0 /，满足F1∩∩Fr≠0 /。我们证明存在εr> 0和nr使得| F | ≤（r +1）（k-r n-r-1）+（k-r-1 n-r-1）对所有n和k均成立，满足n> nr和| k / n-1/2 | <εr。
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