Theorems · Theorem · measure theory
MeasureTheory.Integrable.measure_norm_gt_lt_top
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
{f : α → β}, MeasureTheory.Integrable f μ → ∀ {ε : ℝ}, 0 < ε → μ {x | ε < ‖f x‖} < ⊤A non-quantitative version of Markov inequality for integrable functions: the measure of points
where ‖f x‖ > ε is finite for all positive ε.
- Cited by
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- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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Cites16
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.ofPredstatement and proof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- LT.lt.leproof · cited by 2,189
- MeasureTheory.Integrablestatement and proof · cited by 1,367
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