Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.measure_support_lt_top_of_lintegral_ne_top
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : MeasureTheory.SimpleFunc α ENNReal},
f.lintegral μ ≠ ⊤ → μ (Function.support ⇑f) < ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Function.supportstatement · cited by 610
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.lintegralstatement and proof · cited by 55
- MeasureTheory.SimpleFunc.finMeasSupp_iffproof · cited by 6
- MeasureTheory.SimpleFunc.FinMeasSupp.of_lintegral_ne_topproof · cited by 4
- MeasureTheory.SimpleFunc.measure_support_lt_topproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_support_eapprox_lt_topproof · cited by 1