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
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
For example, a differentiable nowhere monotone function
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
NisanNisan (1991) pointed out that for monotone functions
sensitivity and block sensitivity are the same.