| ℝd | Euclidean space: ℝd = {x = (x1, …, xd) : ∀i, xi ∈ ℝ} |
| |x| | Euclidean norm: |
| x · y | Euclidean scalar product: x · y = x1y1 + … + xdyd |
| ei | ith basis vector of ℝd |
| Ω | domain on which a function ƒ is defined |
| Ω D | domain of f ⋄ μ: ΩD = {x : x + D ⊂ Ω}, and its figure |
| Ω1/n | Ω with a neighborhood of the boundary of size 1/n removed |
| | Ω1/n truncated by |
| | part of Ω1/n which is star-shaped with respect to a, and its figure |
| | potato-shaped set: |
| κn | crown-shaped set: |
| ω | subset of ℝd |
| |ω| | Lebesgue measure of the open set ω |
| σ | negligible subset of ℝd |
| B(x, r) | closed ball B(x, r) = {y ∈ ℝd : |y − x| ≤ r} |
| Ḃ(x, r) | open ball Ḃ(x, r) = {y ∈ ℝd : |y − x| < r} |
| υd | measure of the unit ball: υd = |Ḃ(0, 1)| |
| C(x, p, r) | open crown C(x, p, r) = {y ∈ ℝd : ρ < |y − x| < r} |
| S(x,r) | sphere: S(x, r) = {y ∈ ℝd : |y − x| = r} |
| Δs,n | closed cube of edge length 2−n centered at 2−ns |
| P(υ1,…, υd) | open parallelepiped with edges υ1, …, υd |
