Theorems · Theorem · measure theory
MeasureTheory.integrable_resolvent
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : MeasurableSpace 𝕜] [CompleteSpace 𝕜]
[inst_3 : NormedDivisionRing A] [inst_4 : NormedAlgebra 𝕜 A] [HereditarilyLindelofSpace 𝕜] [OpensMeasurableSpace 𝕜]
[CompleteSpace A] [SecondCountableTopology A] [inst_9 : MeasurableSpace A] [BorelSpace A]
{μ : MeasureTheory.Measure 𝕜} [MeasureTheory.IsFiniteMeasure μ] {a : A},
a ∉ ⇑(algebraMap 𝕜 A) '' μ.support → MeasureTheory.Integrable (resolvent a) μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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 · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- RingHomstatement · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.imagestatement and proof · cited by 5,609
- Algebra.algebraMapstatement and proof · cited by 4,706
- CompleteSpacestatement and proof · cited by 2,532
- Filter.univ_mem'proof · cited by 1,672
- BorelSpacestatement and proof · cited by 1,602
- Filter.mp_memproof · cited by 1,537
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.hasDerivAt_resolventTransformproof · cited by 1