Outer measure: Difference between revisions

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* <math> \mu^* ( \emptyset) = 0 </math>,
* <math> \mu^* ( \emptyset) = 0 </math>,
* <math> \mu^*(A) \leq \mu^*(B)</math> if <math> A \subseteq B</math>,
* <math> \mu^*(A) \leq \mu^*(B)</math> if <math> A \subseteq B</math>,
* <math> \mu* (\cup_{j=1}^\infty A_j) \leq  \sum_{j=1}^\infty \mu^*(A_j).</math>
* <math> \mu^* (\cup_{j=1}^\infty A_j) \leq  \sum_{j=1}^\infty \mu^*(A_j).</math>




==References==
==References==

Revision as of 17:48, 20 October 2020

Let be a nonempty set. An outer measure [1] on the set is a function such that

  • ,
  • if ,


References

  1. Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, second edition, Section 1.4