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Theorems · Theorem · global analysis

ExistsContDiffBumpBase.u_int_pos

∀ (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],
  0 < ∫ (x : E), ExistsContDiffBumpBase.u x ∂MeasureTheory.Measure.addHaar
Defined in
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
Cited by
4 results in Mathlib
Foundations
Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceFiniteDimensionalMeasurableSpaceBorelSpace
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Around this declaration

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

ExistsContDiffBumpBase.w_support · cited by 4ExistsContDiffBumpBase.w_…ExistsContDiffBumpBase.w_integral · cited by 2ExistsContDiffBumpBase.w_…ExistsContDiffBumpBase.w_nonneg · cited by 2ExistsContDiffBumpBase.w_…ExistsContDiffBumpBase.y_smooth · cited by 0ExistsContDiffBumpBase.y_…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceFiniteDimensional · cited by 1854FiniteDimensionalMeasureTheory.integral · cited by 1779MeasureTheory.integralBorelSpace · cited by 1602BorelSpacezero_lt_one · cited by 598zero_lt_oneMeasureTheory.Measure.addHaar · cited by 26Measure.addHaarContinuous.integrable_of_hasCompactSupport · cited by 18Continuous.integrable_of_…ExistsContDiffBumpBase.u · cited by 14ExistsContDiffBumpBase.uMeasureTheory.integral_pos_iff_support_of_nonneg · cited by 9MeasureTheory.integral_po…Metric.measure_ball_pos · cited by 5Metric.measure_ball_posExistsContDiffBumpBase.u_int_…CITED BYCITES

Cites19

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

Cited by4

Results whose statement or proof uses this declaration.