Definition:Monotone

Disambiguation

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Monotone may refer to:

• Mappings:
  • Monotone (Order Theory): A mapping from one ordered set to another is monotone if and only if it is either increasing or decreasing.
  • Monotone (Measure Theory): A mapping $f: \SS \to \R$ on an algebra of sets $\SS$ is monotone if and only if $A \subseteq B \iff \map f A \le \map f B$.

• Monotone Class: A collection of subsets closed under countable intersections and unions.
• Definition:Monotone Galois Connection

In all cases, the sense is one of changing always in the same direction.

Also see

• Definition:Antitone

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): monotonic (monotone)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): monotonic (monotone)