Theorems · Theorem · probability
ProbabilityTheory.gaussianReal_of_var_ne_zero
∀ (μ : ℝ) {v : NNReal},
v ≠ 0 → ProbabilityTheory.gaussianReal μ v = MeasureTheory.volume.withDensity (ProbabilityTheory.gaussianPDF μ v)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 244 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 · cited by 10,939
- NNRealstatement and proof · cited by 4,310
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- MeasureTheory.Measure.withDensitystatement · cited by 265
- ProbabilityTheory.gaussianRealstatement · cited by 77
- ProbabilityTheory.gaussianPDFstatement · cited by 18
Cited by7
Results whose statement or proof uses this declaration.
- MeasurableEquiv.gaussianReal_map_symm_applyproof · cited by 2
- ProbabilityTheory.nullSingletonClass_gaussianRealproof · cited by 2
- ProbabilityTheory.gaussianReal_applyproof · cited by 1
- ProbabilityTheory.rnDeriv_gaussianRealproof · cited by 0
- MeasurableEmbedding.gaussianReal_comap_applyproof · cited by 0
- ProbabilityTheory.gaussianReal_absolutelyContinuousproof · cited by 0
- ProbabilityTheory.gaussianReal_absolutelyContinuous'proof · cited by 0