On Luzinʼs (N)-Property of the Sum of Two Functions

Dušan Pokorný

doi:rae/1209398375

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Home > Journals > Real Anal. Exchange > Volume 33 > Issue 1 > Article

2007/2008 On Luzinʼs (N)-Property of the Sum of Two Functions

Dušan Pokorný

Real Anal. Exchange 33(1): 23-28 (2007/2008).

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Abstract

We prove that, for any nonconstant continuous function $f,$ there exists a continuous N-function $g$ such that $f+g$ is not an N-function. This answers a query by F. S. Cater.