Theorems · Theorem · functional analysis
MeasureTheory.memLp_zero_iff_aestronglyMeasurable
∀ {α : Type u_1} {ε : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : ENorm ε]
[inst_1 : TopologicalSpace ε] {f : α → ε}, MeasureTheory.MemLp f 0 μ ↔ MeasureTheory.AEStronglyMeasurable f μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENormTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topproof · cited by 9,680
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.MemLpstatement · cited by 457
- ENormstatement and proof · cited by 155
- MeasureTheory.eLpNorm_exponent_zeroproof · cited by 43
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
- MeasureTheory.SimpleFunc.memLp_of_finite_measure_preimageproof · cited by 1
- MeasureTheory.SimpleFunc.memLp_zeroproof · cited by 0