nondecreasing

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1: 1.4 Calculus of One Variable

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§1.4(i) Monotonicity

►If $f(x_1)\le f(x_2)$ for every pair $x_1$, $x_2$ in an interval $I$ such that , then $f(x)$ is nondecreasing on $I$. … ►If $f^{\prime }(x)\ge 0$ ($\le 0$) ($=0$) for all $x\in (a,b)$, then $f$ is nondecreasing (nonincreasing) (constant) on $(a,b)$. … ►In this case, $g(x)={𝒱}_{a,x}\left(f\right)$ and $h(x)={𝒱}_{a,x}\left(f\right)-f(x)$ are nondecreasing bounded functions and $f(x)=g(x)-h(x)$. …

2: 18.2 General Orthogonal Polynomials

… ►More generally than (18.2.1)–(18.2.3), $w(x)dx$ may be replaced in (18.2.1) by a positive measure $d\alpha (x)$, where $\alpha (x)$ is a bounded nondecreasing function on the closure of $(a,b)$ with an infinite number of points of increase, and such that for all $n$. …

3: 2.8 Differential Equations with a Parameter

… ►The regions of validity ${\mathbf{\Delta }}_j({\alpha }_j)$ comprise those points $\xi$ that can be joined to ${\alpha }_j$ in $\mathbf{\Delta }$ by a path ${𝒬}_j$ along which $\mathrm{\Re }v$ is nondecreasing $(j=1)$ or nonincreasing $(j=2)$ as $v$ passes from ${\alpha }_j$ to $\xi$. …