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
Focal cloud Focal cloud A focal cloud is the collection of focal points of an "imperfect" lens or parabolic reflector whether optical, electrostatic or electromagnetic. This includes parabolic antennas and lens-type reflective antennas of all kinds. The effect is analogous to the circle of confusion in photography. In a perfect lens or parabolic reflector, rays parallel to the device's axis striking the lens or reflector all pass through a single point, the focal point. In an imperfectly constructed lens or reflector, rays passing through different parts of the element do not converge to a single point but have different focal points. The