<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Using partitions of the unity ((<italic>PU</italic>)-partition), a new definition of an integral is given for a function <italic>f </italic>: [<italic>a, b</italic>] →</p><p><italic> X</italic>, where <italic>X </italic>is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.</p></abstract>

Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.

An integral for a banach valued function

Dipartimento di Matematica Universit´a di Palermo Via Archirafi 34 90123 Palermo ITALY

Tatra Mountains Mathematical Publications

{"article-title":"An integral for a banach valued function"}

Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is...

An integral for a banach valued function

Published Online: Nov 12, 2012

Page range: 105 - 113

DOI: https://doi.org/10.2478/v10127-009-0051-4

Keywords
Banach valued function, (PU)-partition, (PU)∗-integral, Bochner-integral.

This content is open access.

An integral for a banach valued function

Published Online: Nov 12, 2012

Page range: 105 - 113

DOI: https://doi.org/10.2478/v10127-009-0051-4

KeywordsBanach valued function, (PU)-partition, (PU)∗-integral, Bochner-integral.

This content is open access.

Keywords
Banach valued function, (PU)-partition, (PU)∗-integral, Bochner-integral.