Theorems · Theorem · functional analysis
MeasureTheory.memLp_congr_ae
∀ {α : Type u_1} {ε : Type u_2} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} [inst : ENorm ε]
[inst_1 : TopologicalSpace ε] {f g : α → ε}, f =ᵐ[μ] g → (MeasureTheory.MemLp f p μ ↔ MeasureTheory.MemLp g p μ)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 209 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.
Cites13
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 and proof · cited by 9,879
- Top.topproof · cited by 9,680
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.AEStronglyMeasurableproof · cited by 755
- MeasureTheory.MemLpstatement · cited by 457
- MeasureTheory.eLpNormproof · cited by 329
- ENormstatement and proof · cited by 155
- MeasureTheory.eLpNorm_congr_aeproof · cited by 48
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.ae_eqproof · cited by 9
- MeasureTheory.MemLp.aefinStronglyMeasurableproof · cited by 3
- MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_leproof · cited by 1
- ContinuousMap.memLpproof · cited by 0