An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.
"A Birkhoff Type Integral and the Bourgain Property in a Locally Convex Space." Real Anal. Exchange 32 (2) 409 - 428, 2006/2007.