Logarithmically concave measure Logarithmically concave measure In mathematics, a Borel measure "μ" on "n"-dimensional Euclidean space formula_1 is called logarithmically concave (or log-concave for short) if, for any compact subsets "A" and "B" of formula_1 and 0 < "λ" < 1, one has where "λ" "A" + (1 − "λ") "B" denotes the Minkowski sum of "λ" "A" and (1 − "λ") "B". The Brunn–Minkowski inequality asserts that the Lebesgue measure is log-concave. The restriction of the Lebesgue measure to any convex set is also log-concave. By a theorem of Borell, a measure is log-concave if and only if it has a density
Parallel projection Parallel projection A parallel projection is a projection of an object in three-dimensional space onto a fixed plane, known as the "projection plane" or "image plane", where the "rays", known as "lines of sight" or "projection lines", are parallel to each other. It is a basic tool in descriptive geometry. The projection is called "orthographic" if the rays are perpendicular (orthogonal) to the image plane, and "oblique" or "skew" if they are not. A parallel projection is a particular case of "projection" in mathematics and "graphical projection" in technical drawing. Parallel projections can be seen as the limit of a