A gliding hump property for the Henstock-Kurzweil integral (Q1304203)

A gliding hump property for the space \(H\) of Henstock-Kurzweil integrable vector-valued functions, which is not a complete normed space, is established. The property established is more complicated since the integral is nonabsolute. The barrelledness of the space \(H\) is proved by using the gliding hump property along with the matrix theorem of Antosik and Mikusiński. The real-valued case is known and was first proved by Sargent whereas the vector-valued case proved here seems to be new.