Difference between revisions of "Monotonic set function"

Latest revision as of 14:18, 18 March 2015

Sometimes called Monotone set function.

Definition

A set function $f:E\rightarrow [0,\infty]\subset\mathbb{R}$ is monotonic^[1] if for $A,B\in E$ we have $A\subseteq B\implies f(A)\le f(B)$

We do not require a function that maps to $[0,\infty]$ any linearly ordered set will do. It will likely be encountered in this form though.

See also

• Subtractive set function

References

1. Jump up ↑ p37 - Halmos, Measure Theory, Springer Texts in mathematics - book 18