Lebesgue Measure

The Lebesgue measure \(\lambda\) on \(\mathbb{R}^d\) is the canonical measure on the measurable space \((\mathbb{R}^d, \Sigma)\) (where \(\Sigma\) is the Borel $σ$-algebra generated by the standard topology on \(\mathbb{R}^d\) induced by the Euclidean norm).