The Denjoy extension of the Riemann and McShane integrals

Title:

The Denjoy extension of the Riemann and McShane integrals

Creator:

Park, Jae Myung

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8803e9c1-6274-4dfb-af35-b66f981d7efb
uuid:8803e9c1-6274-4dfb-af35-b66f981d7efb

Subject:

math, Denjoy-Riemann integral, and Denjoy-McShane integral

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval $\left[ a,b\right] $ into a Banach space $X.$ It is shown that a Denjoy-Bochner integrable function on $ \left[ a,b\right] $ is Denjoy-Riemann integrable on $\left[ a,b\right] $, that a Denjoy-Riemann integrable function on $\left[ a,b\right] $ is Denjoy-McShane integrable on $\left[ a,b\right] $ and that a Denjoy-McShane integrable function on $\left[ a,b\right] $ is Denjoy-Pettis integrable on $\left[ a,b\right].$ In addition, it is shown that for spaces that do not contain a copy of $c_{0}$, a measurable Denjoy-McShane integrable function on $\left[ a,b\right] $ is McShane integrable on some subinterval of $\left[ a,b\right].$ Some examples of functions that are integrable in one sense but not another are included.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

615-625

Source:

Czechoslovak Mathematical Journal | 2000 Volume:50 | Number:3

Harvested from:

CDK

Metadata only:

false