Theorems · Theorem · functional analysis
MeasureTheory.memLp_top_of_bound
∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
{f : α → E},
MeasureTheory.AEStronglyMeasurable f μ → ∀ (C : ℝ), (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ C) → MeasureTheory.MemLp f ⊤ μ- Cited by
- 11 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- 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
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.MemLpstatement · cited by 457
- MeasureTheory.eLpNorm_exponent_topproof · cited by 36
Cited by11
Results whose statement or proof uses this declaration.
- Continuous.memLp_top_of_hasCompactSupportproof · cited by 5
- MeasureTheory.Integrable.bdd_smulproof · cited by 4
- ContinuousLinearMap.integrable_of_bilin_of_bdd_leftproof · cited by 3
- MeasureTheory.MemLp.condExpproof · cited by 3
- LipschitzWith.memLp_lineDerivproof · cited by 2
- integrableOn_peak_smul_of_integrableOn_of_tendstoproof · cited by 2
- MeasureTheory.Integrable.smul_bddproof · cited by 2
- SchwartzMap.memLp_topproof · cited by 1
- MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_subproof · cited by 1
- MeasureTheory.SimpleFunc.memLp_topproof · cited by 1
- HasCompactSupport.memLp_of_boundproof · cited by 0