Theorems · Theorem · global analysis

ContDiffBump.tsupport_normed_eq

∀ {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],
  tsupport (f.normed μ) = Metric.closedBall c f.rOut

Defined in: Mathlib.Analysis.Calculus.BumpFunction.Normed
Cited by: 1 results in Mathlib
Foundations: Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace HasContDiffBump MeasurableSpace BorelSpace FiniteDimensional MeasureTheory.IsLocallyFiniteMeasure MeasureTheory.Measure.IsOpenPosMeasure

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Cites21

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

Setstatement and proof · cited by 53,352
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
FiniteDimensionalstatement and proof · cited by 1,854
BorelSpacestatement and proof · cited by 1,602
LT.lt.ne'proof · cited by 1,417
closureproof · cited by 1,254
Metric.closedBallstatement and proof · cited by 704
tsupportstatement · cited by 178

Cited by1

Results whose statement or proof uses this declaration.

ContDiffBump.hasCompactSupport_normedproof · cited by 1