Many mathematicians may never have heard of Bernstein functions, because in probability they are known as Laplace exponents, in harmonic analysis as negative definite functions, in complex analysis as Pick or Nevanlinna functions, and in matrix analysis and operator theory as monotone function
By (ii), we know that [xi] = [xi](x) is a monotone function
Of the calibration curves, 62-90% were best fit via the MONOTONE function
(lowest absolute SSRs), and 9-28% by MOD4P.
With LD, to get E(p) a strictly monotone function
requires a market supply function S(p) with [-S(p)] monotone.
A production function f is called quasi-sum if there exist strict monotone functions
Many mathematicians may not have heard of Berstein functions, because in many branches of the field, they are called different names: Laplace exponents, negative definite functions, Pick or Nevanlinna functions, operator monotone functions
, and so on.
In the article by Frank Hansen the remarkable new applications of operator monotone functions
in economics are developed, involving two notions in microeconomics, decreasing relative risk premium and risk vulnerability.
Let us remark that the set of Stieltjes transforms is a subset of the set of completely monotone functions
In the next section we demonstrate that a broad class of preferences introduced in  are represented by matrix monotone functions of order 2.
The main result in this section is that operator monotone functions are risk vulnerable.
algebras as discussed in the case of monotone functions
by [2, Theorem 5; 9, Theorem 2.