Monotonic set function
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Sometimes called Monotone set function.
Definition
A set function f:E→[0,∞]⊂R is monotonic[1] if for A,B∈E we have A⊆B⟹f(A)≤f(B)
We do not require a function that maps to [0,∞] any linearly ordered set will do. It will likely be encountered in this form though.
See also
References
- Jump up ↑ p37 - Halmos, Measure Theory, Springer Texts in mathematics - book 18
