monotone function

Definitions

1. 1

   A function f

   A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).

   • Where defined, the first derivative of a monotone function never changes sign, although it may be zero.
   • Section 1 contains Lebesgue's main tool, a theorem saying that monotone functions on the line are differentiable almost everywhere.
2. 2

   A Boolean function with the property that switching any one input variable from 0 to 1…

   A Boolean function with the property that switching any one input variable from 0 to 1 results either in no change in output or a change from 0 to 1.

The neighborhood

• neighbormonotone
• neighbormonotone operator
• neighbormonotone transformation
• neighbormonotonic
• neighborabsolutely monotonic
• neighborstrictly decreasing
• neighborstrictly increasing
• neighborweakly decreasing
• neighborweakly increasing
• neighborfunction
• neighborisotone function
• neighbororder-preserving function