Theorems · Theorem · global analysis
ContDiffBump.integral_normed
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : HasContDiffBump E]
[inst_3 : MeasurableSpace E] {c : E} (f : ContDiffBump c) {μ : MeasureTheory.Measure E} [BorelSpace E]
[FiniteDimensional ℝ E] [MeasureTheory.IsLocallyFiniteMeasure μ] [μ.IsOpenPosMeasure], ∫ (x : E), f.normed μ x ∂μ = 1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- mul_commproof · cited by 2,262
- FiniteDimensionalstatement and proof · cited by 1,854
- MeasureTheory.integralstatement and proof · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
- LT.lt.ne'proof · cited by 1,417
- div_eq_mul_invproof · cited by 715
- inv_mul_cancel₀proof · cited by 267
Cited by4
Results whose statement or proof uses this declaration.
- ContDiffBump.integral_normed_smulproof · cited by 1
- ContDiffBump.convolution_tendsto_rightproof · cited by 1
- ContDiffBump.dist_normed_convolution_leproof · cited by 1
- ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrableproof · cited by 0