Theorems · Definition · global analysis
ExistsContDiffBumpBase.y
{E : Type u_1} →
[inst : NormedAddCommGroup E] →
[inst_1 : NormedSpace ℝ E] → [FiniteDimensional ℝ E] → [inst_3 : MeasurableSpace E] → [BorelSpace E] → ℝ → E → ℝAn auxiliary function to construct partitions of unity on finite-dimensional real vector spaces.
It is the convolution between a smooth function of integral 1 supported in the ball of radius D,
with the indicator function of the closed unit ball. Therefore, it is smooth, equal to 1 on the
ball of radius 1 - D, with support equal to the ball of radius 1 + D.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- FiniteDimensionalstatement and proof · cited by 1,854
- BorelSpacestatement and proof · cited by 1,602
- ContinuousLinearMap.lsmulproof · cited by 66
- MeasureTheory.convolutionproof · cited by 65
- MeasureTheory.Measure.addHaarproof · cited by 26
- ExistsContDiffBumpBase.wproof · cited by 11
- ExistsContDiffBumpBase.φproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.y_eq_zero_of_notMem_ballstatement · cited by 1
- ExistsContDiffBumpBase.y_pos_of_mem_ballstatement · cited by 1
- ExistsContDiffBumpBase.y_eq_one_of_mem_closedBallstatement · cited by 0
- ExistsContDiffBumpBase.y_le_onestatement · cited by 0
- ExistsContDiffBumpBase.y_negstatement · cited by 0
- ExistsContDiffBumpBase.y_nonnegstatement · cited by 0
- ExistsContDiffBumpBase.y_smoothstatement · cited by 0
- ExistsContDiffBumpBase.y_supportstatement · cited by 0
- ExistsContDiffBumpBase.y.congr_simpstatement and proof · cited by 0