This is an announcement for the paper "Compactness in the Lebesgue-Bochner spaces L^p(\mu;X)" by Jan van Neerven. Abstract: Let (\Omega,\mu) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L^p(\mu;X) is relatively compact if and only if it is uniformly p-integrable, uniformly tight, and scalarly relatively compact. Archive classification: math.FA Mathematics Subject Classification: Primary: 46E40, Secondary: 46E30, 46B50 Remarks: 5 pages, submitted for publication Submitted from: J.M.A.M.vanNeerven@tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.5688 or http://arXiv.org/abs/1305.5688