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Статья

A selection principle for functions of a real variable

Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia. 2005. Vol. 53. No. 1. P. 25-43.

We present a new sufficient condition (which turns out to be almost necessary) in terms of the modulus of variation in order for a given sequence of real valued functions, defi ned on a closed interval, to contain a pointwise convergent subsequence whose limit is a bounded function with simple discontinuities. We show that many Helly type selection theorems, having to do with uniform boundedness of generalized variations, are consequences of our result.