Theorems · Theorem · global analysis
ExistsContDiffBumpBase.w_def
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
[inst_3 : MeasurableSpace E] [inst_4 : BorelSpace E] (D : ℝ),
ExistsContDiffBumpBase.w D = fun x =>
((∫ (x : E), ExistsContDiffBumpBase.u x ∂MeasureTheory.Measure.addHaar) * |D| ^ Module.finrank ℝ E)⁻¹ •
ExistsContDiffBumpBase.u (D⁻¹ • x)- Cited by
- 2 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.
Cites12
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
- absstatement · cited by 1,814
- MeasureTheory.integralstatement · cited by 1,779
- Module.finrankstatement · cited by 1,770
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.Measure.addHaarstatement · cited by 26
- ExistsContDiffBumpBase.ustatement · cited by 14
- ExistsContDiffBumpBase.wstatement and proof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.w_supportproof · cited by 4
- ExistsContDiffBumpBase.y_negproof · cited by 0