Distances to spaces of measurable and integrable functions (Q2862556)

The authors summarize the content of this paper in the following abstract: Given a complete probability space \((\Omega, \Sigma, \mu)\) and a Banach space \(X\) we establish formulas to compute the distance from a function \(f \in X^\Omega\) to the spaces of strongly measurable and Bochner integrable functions. We study the relationship between these distances and use them to prove some quantitative counterparts of Pettis' measurability theorem. We also give several examples showing that some of our estimates are sharp.