Theorems · Theorem · global analysis
ContDiffBump.nonneg_normed
∀ {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} (x : E), 0 ≤ f.normed μ x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- div_nonnegproof · cited by 103
- ContDiffBumpstatement and proof · cited by 61
- MeasureTheory.integral_nonnegproof · cited by 52
- HasContDiffBumpstatement and proof · cited by 46
- ContDiffBump.normedstatement · cited by 22
- ContDiffBump.nonnegproof · cited by 6
- ContDiffBump.nonneg'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ContDiffBump.convolution_tendsto_rightproof · cited by 1
- ContDiffBump.dist_normed_convolution_leproof · cited by 1
- ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrableproof · cited by 0