Theorems · Theorem · probability
ProbabilityTheory.paretoPDFReal_nonneg
∀ {t r : ℝ}, 0 ≤ t → 0 ≤ r → ∀ (x : ℝ), 0 ≤ ProbabilityTheory.paretoPDFReal t r xThe Pareto pdf is nonnegative.
- Defined in
- Mathlib.Probability.Distributions.Pareto
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- lt_of_lt_of_leproof · cited by 438
- mul_nonnegproof · cited by 397
- Real.rpow_pos_of_posproof · cited by 155
- Real.rpow_nonnegproof · cited by 111
- le_iff_eq_or_ltproof · cited by 20
- ProbabilityTheory.paretoPDFRealstatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cdf_paretoMeasure_eq_integralproof · cited by 0