Theorems · Theorem · global analysis
ContDiffBump.measure_closedBall_le_integral
∀ {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.real (Metric.closedBall c f.rIn) ≤ ∫ (x : E), ↑f x ∂μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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_oneproof · cited by 3,885
- FiniteDimensionalstatement and proof · cited by 1,854
- MeasureTheory.integralstatement · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
- Metric.closedBallstatement and proof · cited by 704
- MeasureTheory.Measure.realstatement and proof · cited by 530
- Filter.Eventually.of_forallproof · cited by 526
Cited by2
Results whose statement or proof uses this declaration.
- ContDiffBump.measure_closedBall_div_le_integralproof · cited by 1
- ContDiffBump.normed_le_div_measure_closedBall_rInproof · cited by 0