# Subtractive set function

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## Definition

A set function [math]f:E\rightarrow[0,\infty]\subset\mathbb{R}\cup\{-\infty,\infty\}[/math] is subtractive^{[1]} if whenever [ilmath]A,B\in E[/ilmath] we have

[math]A\subseteq B\wedge B-A\in E\wedge |f(B)|<\infty\implies f(B-A)=f(B)-f(A)[/math]

## See also

## References

- ↑ p37 - Halmos - Measure Theory - Graduate Texts in Mathematics - 18