Abstract
We introduce a class of continuous completely regular functions satisfying the N-property. We obtain a decomposition of an arbitrary continuous function into the sum of two functions the first of which is completely regular and the second does not enjoy the N-property. We define a class of strongly regular Borel functions for which we prove the Luzin N-property. We demonstrate that the image of every Lebesgue measurable set of a strongly regular function is measurable. From an arbitrary Borel function we extract a strongly regular function and a function that does not enjoy the N-property.
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Nasyrov, F.S. Function Decompositions Related to the Luzin N-property. Siberian Mathematical Journal 45, 146–154 (2004). https://doi.org/10.1023/B:SIMJ.0000013020.30432.7e
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DOI: https://doi.org/10.1023/B:SIMJ.0000013020.30432.7e