Theorems · Theorem · probability
ProbabilityTheory.gaussianReal_apply
∀ (μ : ℝ) {v : NNReal},
v ≠ 0 → ∀ (s : Set ℝ), (ProbabilityTheory.gaussianReal μ v) s = ∫⁻ (x : ℝ) in s, ProbabilityTheory.gaussianPDF μ v x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ProbabilityTheory.gaussianRealstatement · cited by 77
- ProbabilityTheory.gaussianPDFstatement and proof · cited by 18
- MeasureTheory.withDensity_apply'proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.gaussianReal_apply_eq_integralproof · cited by 2