## Illinois Journal of Mathematics

### When do McShane and Pettis integrals coincide?

#### Abstract

We give a partial answer to the question in the title by showing that the McShane and Pettis integrals coincide for functions with values in super-reflexive spaces as well as for functions with values in $c_0(\Gamma)$. We also improve an example of Fremlin and Mendoza, according to which these integrals do not coincide in general, by showing that, at least under the Continuum Hypothesis, there is a scalarly negligible function which is not McShane integrable.

#### Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1177-1187.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138098

Digital Object Identifier
doi:10.1215/ijm/1258138098

Mathematical Reviews number (MathSciNet)
MR2036997

Zentralblatt MATH identifier
1045.28006

#### Citation

Di Piazza, L.; Preiss, D. When do McShane and Pettis integrals coincide?. Illinois J. Math. 47 (2003), no. 4, 1177--1187. doi:10.1215/ijm/1258138098. https://projecteuclid.org/euclid.ijm/1258138098