The additive measure of a subset is less or equal to its superset

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Concept

Proof

Let , , and finally .

We can write

and because is additive:

Then the measure of is either infinite or finite, which in turn implies:

In both cases .

Therefore,

Examples

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Appendix

• Tags:
  • Measure Theory, Measure Functions
• Reference:
  • ; Measure Theory Lecture 2
• Related:
  • Additive Measure Functions

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