Multidimensional Lusin-type inequalities for Grand Lebesgue Spaces

TL;DR

This paper extends classical Lusin's theorem to multidimensional settings within Grand Lebesgue Spaces, broadening the understanding of integral existence for measurable functions in these advanced function spaces.

Contribution

It introduces multidimensional Lusin-type inequalities specifically tailored for Grand Lebesgue Spaces, expanding the theoretical framework of rearrangement invariant spaces.

Findings

Established multidimensional Lusin-type inequalities for Grand Lebesgue Spaces

Generalized classical Lusin's theorem to a broader class of function spaces

Enhanced understanding of integral properties in advanced function spaces

Abstract

We generalize in this short paper the classical Luzin's theorem about existence of integral on the measurable function and its multidimensional analogues on the many popular classes of rearrangement invariant (r.i.) spaces, namely, on the so-called Grand Lebesgue Spaces.