Convex measure same thing as it being a logarithmically concave measure. The classes of "s"-convex measures form a nested increasing family as "s" decreases to −∞" or, equivalently Thus, the collection of −∞-convex measures is the largest such class, whereas the 0-convex measures (the logarithmically concave measures) are the smallest class. The convexity of a measure "μ" on "n"-dimensional Euclidean space R in the sense above is closely related to the convexity of its probability density function. Indeed, "μ" is "s"-convex if and only if there is an absolutely continuous measure "ν" with probability density function "ρ" on some R so that
Lens (optics) object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length "f" are focused at a point with distance from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped