Theorems · Theorem · probability
ProbabilityTheory.cdf_nonneg
∀ (μ : MeasureTheory.Measure ℝ) (x : ℝ), 0 ≤ ↑(ProbabilityTheory.cdf μ) x
The cdf is non-negative.
- Defined in
- Mathlib.Probability.CDF
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.prodproof · cited by 353
- MeasureTheory.Measure.diracproof · cited by 210
- StieltjesFunction.toFunstatement · cited by 120
- ProbabilityTheory.cdfstatement · cited by 19
- ProbabilityTheory.condCDF_nonnegproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cdf_eq_realproof · cited by 5