On a theorem of E. Helly

E. Helly's theorem asserts that any bounded sequence of monotone real funct ions contains a pointwise convergent subsequence. We reprove this theorem i n a generalized version in terms of monotone functions on linearly ordered sets. We show that the cardinal number responsible for this generalization is exactly the splitting number. We also show that a positive answer to a p roblem of S. Saks is obtained under the assumption of the splitting number being strictly greater than the first uncountable cardinal.