Theorems · Theorem · probability
ProbabilityTheory.isGaussian_of_isGaussian_map
∀ {E : Type u_1} [inst : TopologicalSpace E] [inst_1 : AddCommMonoid E] [inst_2 : Module ℝ E] {mE : MeasurableSpace E}
[OpensMeasurableSpace E] {μ : MeasureTheory.Measure E},
(∀ (L : E →L[ℝ] ℝ), ProbabilityTheory.IsGaussian (MeasureTheory.Measure.map (⇑L) μ)) → ProbabilityTheory.IsGaussian μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidstatement and proof · cited by 12,281
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ContinuousLinearMapstatement and proof · cited by 5,352
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- OpensMeasurableSpacestatement and proof · cited by 636
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isGaussian_of_map_eq_gaussianRealproof · cited by 2