Preiss is a recipient of the Ostrowski Prize (2011) and the winner of the 2008 London Mathematical Society Pólya Prize for his 1987 result on Geometry of Measures, where he solved the remaining problem in the geometric theoretic structure of sets and measures in Euclidean space. He was an invited speaker at the ICM 1990 in Kyoto. He is a Fellow of the Royal Society (2004) and a Foreign Fellow of the Learned Society of the Czech Republic (2003).
- Erdős, Paul; Preiss, David (1976). "Decomposition of Spheres in Hilbert Spaces". Commentationes Mathematicae Universitatis Carolinae. 017 (4): 791–795.
- Preiss, David (1987). "Geometry of measures in R^n: Distribution, rectifiability, and densities". The Annals of Mathematics. 125 (3): 537–643. doi:10.2307/1971410. hdl:10338.dmlcz/133417. JSTOR 1971410.
- Mathematics Staff and Postgraduates, University of Warwick Institute of Mathematics. Revised 2 March 2012. Retrieved 26 October 2015.
- "List of LMS prize winners". London Mathematical Society. Retrieved 26 October 2015.
- London Mathematical Society Prizes 2008, London Mathematical Society, Media release, 4 July 2008. Retrieved 26 October 2015.
- Editorial Board, Real Analysis Exchange. Retrieved 26 October 2015.