summary: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.
展开▼
机译：摘要：在本文中，我们研究了将区间$ \ left [a，b \ right] $映射到Banach空间$ X中的函数的Denjoy-Riemann和Denjoy-McShane积分。证明了Denjoy-Bochner可积函数在$ \ left [a，b \ right] $上，是$ \ left [a，b \ right] $上的Denjoy-Riemann可积，在$ \ left [a，b \ right] $上的Denjoy-Riemann可积函数是Denjoy-McShane可积在$ \ left [a，b \ right] $上，并且Denjoy-McShane可积函数在$ \ left [a，b \ right] $上是Denjoy-Pettis可积在$ \ left [a，b \右]。$另外，对于不包含$ c_ {0} $副本的空间，在$ \ left [a，b \ right] $上可测量的Denjoy-McShane可积函数在$ \ left [a，b \ right] $上是McShane可积$ \ left [a，b \ right]。$的某些子间隔。$包括一些在某种意义上可集成但在另一种意义上不可集成的函数示例。
展开▼
