Mathlib Map

Theorems · Definition · global analysis

ContDiffBump.normed

{E : Type u_1} →
  [inst : NormedAddCommGroup E] →
    [inst_1 : NormedSpace ℝ E] →
      [HasContDiffBump E] → [inst : MeasurableSpace E] → {c : E} → ContDiffBump c → MeasureTheory.Measure E → E → ℝ

A bump function normed so that ∫ x, f.normed μ x ∂μ = 1.

Defined in
Mathlib.Analysis.Calculus.BumpFunction.Normed
Cited by
22 results in Mathlib
Foundations
Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceHasContDiffBumpMeasurableSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContDiffBump.support_normed_eq · cited by 5ContDiffBump.support_norm…ContDiffBump.integral_normed · cited by 4ContDiffBump.integral_nor…ContDiffBump.nonneg_normed · cited by 3ContDiffBump.nonneg_normedContDiffBump.normed_def · cited by 3ContDiffBump.normed_defContDiffBump.tendsto_support_normed_smallSets · cited by 1ContDiffBump.tendsto_supp…ContDiffBump.tsupport_normed_eq · cited by 1ContDiffBump.tsupport_nor…MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le · cited by 1LocallyIntegrable.exists_…ContDiffBump.contDiff_normed · cited by 1ContDiffBump.contDiff_nor…ContDiffBump.convolution_tendsto_right · cited by 1ContDiffBump.convolution_…ContDiffBump.dist_normed_convolution_le · cited by 1ContDiffBump.dist_normed_…ContDiffBump.hasCompactSupport_normed · cited by 1ContDiffBump.hasCompactSu…ContDiffBump.normed.congr_simp · cited by 1normed.congr_simpContDiffBump.integral_normed_smul · cited by 1ContDiffBump.integral_nor…ContDiffBump.normed_le_div_measure_closedBall_rOut · cited by 1ContDiffBump.normed_le_di…ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable · cited by 0ContDiffBump.ae_convoluti…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.integral · cited by 1779MeasureTheory.integralContDiffBump · cited by 61ContDiffBumpHasContDiffBump · cited by 46HasContDiffBumpContDiffBump.toFun · cited by 43ContDiffBump.toFunContDiffBump.normedCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by22

Results whose statement or proof uses this declaration.