📚 noun • entry_id 46363
monotone function
Meanings (ES + gloss)
función monótona
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).
Section 1 contains Lebesgue's main tool, a theorem saying that monotone functions on the line are differentiable almost everywhere.
Where defined, the first derivative of a monotone function never changes sign, although it may be zero.
Phrases
No hay frases
Word forms