Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_pos_iff
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
Measurable f → ∀ {s : Set α}, 0 < ∫⁻ (a : α) in s, f a ∂μ ↔ 0 < μ (Function.support f ∩ s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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 and proof · 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
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.lintegralstatement · cited by 1,152
- Function.supportstatement and proof · cited by 610
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- measurableSet_supportproof · cited by 5
- MeasureTheory.lintegral_pos_iff_supportproof · cited by 1
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