@inbook {IOPORT.02127765, author = {Ratsaby, Joel}, title = {A constrained version of Sauer's lemma.}, year = {2004}, booktitle = {Mathematics and computer science III. Algorithms, trees, combinatorics and probabilities. Proceedings of the international colloquium of mathematics and computer sciences, Vienna, September 13--17, 2004.}, isbn = {3-7643-7128-5}, pages = {543-551}, publisher = {Basel: Birkh\"auser}, abstract = {Summary: We generalize Sauer's Lemma to finite VC-dimension classes ${\cal H}$ of binary-valued functions on $[n]=\{1,\dots,n\}$ which have a margin of at least $N$ on every element in a sample $S\subseteq[n]$ of cardinality $l$, where the margin $\mu_h(x)$ of $h\in{\cal H}$ on a point $x\in[n]$ is defined as the largest non-negative integer $a$ such that $h$ is constant on the interval $I_a(x)= [x-a,x+a]$.}, identifier = {02127765}, }