A Henstock-Kurzweil integrable vector-valued function which is not McShane integrable on any portion

作者：Naralenkov K M^*

来源：Quaestiones Mathematicae, 2012, 35(1): 11-21.

DOI：10.2989/16073606.2012.671160

• Primary 26A39
• 28B05
• Secondary 46G10
• Henstock-Kurzweil
• McShane and McShane-Pettis integrals
• bounded variation
• VB
• AC and ACG functions

We give an example of a function from [a, b] into c(0), which is Henstock-Kurzweil integrable on [a, b] and not McShane integrable on any nondegenerate subinterval of [a, b]. As a result, any Henstock-Kurzweil integrable function from [a, b] into a Banach space X is McShane integrable on some nondegenerate subinterval of [a, b] if and only if X contains no isomorphic copy of c(0).

• 出版日期2012
• 单位国际关系学院