Illinois Journal of Mathematics

When do McShane and Pettis integrals coincide?

L. Di Piazza and D. Preiss

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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

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

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10]
Secondary: 26A39: Denjoy and Perron integrals, other special integrals 26E25: Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx} 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]


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.

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