Theorems · Theorem · measure theory
MeasureTheory.isProbabilityMeasure_tilted
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ} [NeZero μ],
MeasureTheory.Integrable (fun x => Real.exp (f x)) μ → MeasureTheory.IsProbabilityMeasure (μ.tilted f)- Defined in
- Mathlib.MeasureTheory.Measure.Tilted
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
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.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- LT.lt.leproof · cited by 2,189
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.lintegralproof · cited by 1,152
- Real.expstatement and proof · cited by 871
- ENNReal.ofRealproof · cited by 863
- div_eq_mul_invproof · cited by 715
- MeasureTheory.IsProbabilityMeasurestatement · cited by 392
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