Reference Material
The mean width is usually mentioned in any good reference on convex geometry, for instance, Selected topics in convex geometry by Maria Moszyńska (Birkhäuser, Boston 2006). The relation between the mean width and the mean curvature is also derived in that reference.
The application of the mean width as one of the measures featuring in Hadwiger's theorem is discussed in Beifang Chen in "A simplified elementary proof of Hadwiger's volume theorem." Geom. Dedicata 105 (2004), 107—120.
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