A note on $\varrho$-upper continuous functions
Abstract
In the present paper, we introduce the notion of classes of
$\varrho$-upper continuous functions. We show that $\varrho$-upper
continuous functions are Lebesgue measurable and, for
$\varrho<\frac{1}{2}$, may not belong to Baire class 1. We also prove
that a function with Denjoy property can be non-measurable.
$\varrho$-upper continuous functions. We show that $\varrho$-upper
continuous functions are Lebesgue measurable and, for
$\varrho<\frac{1}{2}$, may not belong to Baire class 1. We also prove
that a function with Denjoy property can be non-measurable.
Full Text:
PDFDOI: https://doi.org/10.2478/tatra.v44i0.47