Theorems · Theorem · probability
ProbabilityTheory.geometricMeasure_nonneg
∀ (p : ↑unitInterval) (n : ℕ), 0 ≤ (1 - ↑p) ^ n * ↑p
The positivty tactic does not work for this goal. Use this lemma to rewrite
(ENNReal.ofReal ((1 - p) ^ n * p)).toReal = (1 - p) ^ n * p.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- unitIntervalstatement and proof · cited by 607
- mul_nonnegproof · cited by 397
- pow_nonnegproof · cited by 141
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.hasSum_integral_geometricMeasureproof · cited by 1
- ProbabilityTheory.geometricMeasure_real_singletonproof · cited by 1
- ProbabilityTheory.integrable_geometricMeasure_iffproof · cited by 1
- ProbabilityTheory.integral_geometricMeasureproof · cited by 0