Theorems · Theorem · probability
ProbabilityTheory.lintegral_paretoPDF_eq_one
∀ {t r : ℝ}, 0 < t → 0 < r → ∫⁻ (x : ℝ), ProbabilityTheory.paretoPDF t r x = 1The pdf of the Pareto distribution integrates to 1.
- Defined in
- Mathlib.Probability.Distributions.Pareto
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites50
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- MeasureTheory.aeproof · cited by 2,352
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- Filter.univ_mem'proof · cited by 1,672
- MeasureTheory.Measure.restrictproof · cited by 1,646
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isProbabilityMeasure_paretoMeasureproof · cited by 2