[36] Show that 2C

(a,

b, c) ≤ C

(a, b)+C

(b, c)+C

(c, a)+O(log n)

where n = l(abc).

Comments. For an application relating the three-dimensional volume of a geometric object in Euclidean space to the two-dimensional volumes of its projections, see the discussion in Section 6.14 on page 544. Hint:

use the symmetry of information, Theorem 2.8.2.

Source: [D. Hammer and A.K. Shen, Theor. Comput. Syst., 31:1(1998), 1–4].