A new concept of McShane-tightness is introduced to pass from scalar (alias weak) McShane integrability to Pettis integrability. It is used also to derive a scalar McShane version of the Vitali theorem.
"From Scalar McShane Integrability to Pettis Integrability." Real Anal. Exchange 38 (2) 445 - 466, 2012/2013.