Indeed, suppose that f is a nowhere

monotone function of bounded variation on [0,1].

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 about x.

A

monotone function is obviously monotone-with-fixpoint, but the converse does not necessarily hold.

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.

w](s) is a

monotone function of s [member of] (-[infinity], +[infinity]); if d[bar.

3]) along any line parallel to u, k (x, u) is a

monotone function of x.

For example, a differentiable nowhere

monotone function (see, e.

They cover Hardy's inequality and related topics, some weighted norm inequalities, the Hardy-Stecklov operator, higher order Hardy inequalities, fractional or Hardy inequalities, integral operators on the cone of

monotone functions, and new and complementary results.

A production function f is called quasi-sum if there exist strict

monotone functions F, [h.

NisanNisan (1991) pointed out that for

monotone functions sensitivity and block sensitivity are the same.