View source for Monotonic set function

Sometimes called '''Monotone set function'''. 

==Definition==
A set function {{M|f:E\rightarrow [0,\infty]\subset\mathbb{R} }} is '''monotonic'''<ref>
p37 - Halmos, Measure Theory, Springer Texts in mathematics - book 18
</ref> if for {{M|A,B\in E}} we have {{M|A\subseteq B\implies f(A)\le f(B) }}

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

==See also==
* [[Subtractive set function]]

==References==
{{Definition|Measure Theory}}