Non-Measurable Space

A Non-Measurable Space is a Set Field which members are non-measurable sets.

• • …
• Counter-Example(s):
  • a Measurable Space.
  • a Vector Space.
  • a Distance Metric Space.
• See: Non-Measure Function, Votali Set, Hausdorff paradox, Hausdorff Oaradox, Banach-Tarski Paradox, Lebesgue Measurable.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Measure_(mathematics)#Non-measurable_sets
  • If the axiom of choice is assumed to be true, not all subsets of Euclidean space are Lebesgue measurable; examples of such sets include the Vitali set, and the non-measurable sets postulated by the Hausdorff paradox and the Banach–Tarski paradox.

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