# Questions tagged [lebesgue-measure]

For questions about the Lebesgue measure, a measure defined on the Borel or Lebesgue subsets of the real line or $\mathbb R^d$ for some integer $d$. Use it with (tag: measure-theory) tag and (if necessary) with (tag:lebesgue-integral).

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### Lebesgue measurable but not Borel measurable

I'm trying to find a set which is Lebesgue measurable but not Borel measurable. So I was thinking of taking a Lebesgue set of measure zero and intersecting it with something so that the result is not ...
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### Are most matrices diagonalizable?

More precisely, does the set of non-diagonalizable (over $\mathbb C$) matrices have Lebesgue measure zero in $\mathbb R^{n\times n}$ or $\mathbb C^{n\times n}$? Intuitively, I would think yes, since ...
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### What does it mean for a set to have Lebesgue measure zero?

I am studying examples of sets with Lebesgue measure zero (e.g. the Cantor Set) but wanted an intuitive description of what this means rather than a formal definition. Thank you.
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Consider $\mathbb{Q}$ which is countable, we may enumerate $\mathbb{Q}=\{q_1, q_2, \dots\}$. For each rational number $q_k$, cover it by an open interval $I_k$ centered at $q_k$ with radius $\epsilon/... 3answers 13k views ### What is the difference between outer measure and Lebesgue measure? What is the difference between outer measure and Lebesgue measure? We know that there are sets which are not Lebesgue measurable, whereas we know that outer measure is defined for any subset of$\...
Studying the Lebesgue measure on the line I've found the following argument which concludes that $m(\mathbb{R}) < +\infty$ (where $m$ denotes the Lebesgue measure on $\mathbb{R}$). Obviously it ...