Theorems · Theorem · global analysis
ContDiffBump.integral_le_measure_closedBall
∀ {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],
∫ (x : E), ↑f x ∂μ ≤ μ.real (Metric.closedBall c f.rOut)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites28
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
- Top.topproof · cited by 9,680
- 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
- le_of_ltproof · cited by 1,175
- Metric.closedBallstatement and proof · cited by 704
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