On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous
Tom 114 / 2009
Colloquium Mathematicum 114 (2009), 237-243 MSC: 26A21, 26A15. DOI: 10.4064/cm114-2-6
Let $I\subset \mathbb R$ be an open interval and let $A\subset I$ be any set. Every Baire 1 function $f:I \to \mathbb R$ coincides on $A$ with a function $g:I \to \mathbb R$ which is simultaneously approximately continuous and quasicontinuous if and only if the set $A$ is nowhere dense and of Lebesgue measure zero.