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
Compound refractive lens Compound refractive lens A Compound refractive lens (CRL) is a series of individual lenses arranged in a linear array in order to achieve focusing of X-rays in the energy range of 5-40 keV. They are an alternative to the KB mirror. For all materials the refractive index for X-rays is close to 1, hence a single conventional lens for X-rays has an extremely long focal length (for practical lens sizes). In addition, X-rays attenuate as they pass through a material so that conventional lenses for X-rays have long been considered impractical. The CRL gets its reasonably short focal length, on