Abstract
In the paper infinite information systems are investigated which are used in pattern recognition, discrete optimization, and computational geometry. An information system is called compressible relatively to a weight function if for each problem with enough big weight (total weight of attributes in problem description) there exists a decision tree which solves this problem and which weighted depth is less than the problem weight. In the paper all pairs of information systems and weight functions are described such that the information system is compressible relatively to the weight function.
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