Theorems · Theorem · probability
ProbabilityTheory.betaPDFReal_pos
∀ {α β x : ℝ}, 0 < x → x < 1 → 0 < α → 0 < β → 0 < ProbabilityTheory.betaPDFReal α β xThe beta pdf is positive for all positive reals with positive parameters.
- Defined in
- Mathlib.Probability.Distributions.Beta
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 284 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_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- lt_of_not_geproof · cited by 374
- mul_posproof · cited by 374
- Real.rpow_pos_of_posproof · cited by 155
- one_div_posproof · cited by 27
- ProbabilityTheory.betaPDFRealstatement · cited by 4
- ProbabilityTheory.beta_posproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.lintegral_betaPDF_eq_oneproof · cited by 1