ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4369 on D1744: Lebesgue measure space
Subresult of R1169: Countable euclidean real set has Lebesgue measure zero

Set of euclidean rational numbers has Lebesgue measure zero

Formulation 0

Let $M = (\mathbb{R}^D, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space.

Then

(1)	\begin{equation} \mathbb{Q}^D \in \mathcal{L} \end{equation}
(2)	\begin{equation} \ell(\mathbb{Q}^D) = 0 \end{equation}

Proofs

Proof 0

Let $M = (\mathbb{R}^D, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space.

This result is a particular case of R1169: Countable euclidean real set has Lebesgue measure zero. $\square$