## A generalization of Sauer’s lemma.(English)Zbl 0831.60011

The authors generalize N. Sauer’s lemma [ibid. 13, 145-147 (1972; Zbl 0248.05005)] to multivalued functions, proving tight bounds on the cardinality of subsets of $$\prod^m_{i= 1} \{0,\dots, N_i\}$$ which avoid certain patterns. In addition, the authors give an application of this result, bounding the uniform rate of convergence of empirical estimates of the expectations of a set of random variables to their true expectations.

### MSC:

 60C05 Combinatorial probability 60F05 Central limit and other weak theorems 05A99 Enumerative combinatorics

Zbl 0248.05005
Full Text:

### References:

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