Theorems · Theorem · global analysis
ContDiffBump.integral_pos
∀ {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], 0 < ∫ (x : E), ↑f x ∂μ- Cited by
- 3 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · 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
- MeasureTheory.integralstatement · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
Cited by3
Results whose statement or proof uses this declaration.
- ContDiffBump.support_normed_eqproof · cited by 5
- ContDiffBump.integral_normedproof · cited by 4
- ContDiffBump.normed_le_div_measure_closedBall_rOutproof · cited by 1