Theorems · Theorem · functional analysis
MeasureTheory.eLpNorm_congr_ae
∀ {α : Type u_1} {ε : Type u_2} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} [inst : ENorm ε]
{f g : α → ε}, f =ᵐ[μ] g → MeasureTheory.eLpNorm f p μ = MeasureTheory.eLpNorm g p μ- Cited by
- 48 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENorm
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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.Eventually.monoproof · cited by 646
- MeasureTheory.eLpNormstatement · cited by 329
- ENormstatement and proof · cited by 155
- MeasureTheory.eLpNorm_congr_enorm_aeproof · cited by 3
Cited by48
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.norm_toLpproof · cited by 7
- MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'proof · cited by 5
- MeasureTheory.MemLp.eLpNorm_indicator_leproof · cited by 5
- MeasureTheory.eLpNorm_aeeqFunproof · cited by 4
- MeasureTheory.norm_indicatorConstLpproof · cited by 4
- MeasureTheory.UnifIntegrable.ae_eqproof · cited by 4
- MeasureTheory.memLp_congr_aeproof · cited by 4
- MeasureTheory.Lp.edist_toLp_toLpproof · cited by 4
- MeasureTheory.UniformIntegrable.ae_eqproof · cited by 4
- SchwartzMap.denseRange_toLpCLMproof · cited by 3
- SchwartzMap.norm_toLpproof · cited by 3
- MeasureTheory.uniformIntegrable_ofproof · cited by 3