In this paper we focus on the Lebesgue property of Banach spaces. A real Banach space $X$ is said to have the Lebesgue property if any Riemann integrable function from $[0,1]$ into $X$ is continuous almost everywhere on $[0,1]$. We obtain a partial characterization of the Lebesgue property, showing that it has connections with the asymptotic geometry of the space involved.
"Asymptotic Structure of Banach Spaces and Riemann Integration." Real Anal. Exchange 33 (1) 113 - 126, 2007/2008.