Theorems · Theorem · measure theory
MeasureTheory.tilted_of_not_integrable
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
¬MeasureTheory.Integrable (fun x => Real.exp (f x)) μ → μ.tilted f = 0- Defined in
- Mathlib.MeasureTheory.Measure.Tilted
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- Real.expstatement and proof · cited by 871
- ENNReal.ofRealproof · cited by 863
- zero_smulproof · cited by 716
- MeasureTheory.Measure.withDensityproof · cited by 265
- div_zeroproof · cited by 251
- MeasureTheory.integral_undefproof · cited by 58
- MeasureTheory.Measure.tiltedstatement · cited by 58
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.tilted_of_not_aemeasurableproof · cited by 4
- MeasureTheory.tilted_apply_eq_ofReal_integralproof · cited by 1
- MeasureTheory.tilted_apply_eq_ofReal_integral'proof · cited by 1