## Real Analysis Exchange

### Asymptotic Structure of Banach Spaces and Riemann Integration

K. M. Naralenkov

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 33, Number 1 (2007), 113-126.

Dates
First available in Project Euclid: 28 April 2008