Theorems · Theorem · functional analysis
MeasureTheory.Lp.enorm_def
∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] (f : ↥(MeasureTheory.Lp E p μ)), ‖f‖ₑ = MeasureTheory.eLpNorm (↑↑f) p μ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 223 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- ENorm.enormstatement · cited by 715
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.eLpNormstatement · cited by 329
- ENNReal.coe_toNNRealproof · cited by 53
- MeasureTheory.Lp.eLpNorm_ne_topproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.nnnorm_holder_apply_apply_leproof · cited by 1
- MeasureTheory.enorm_indicatorConstLp_leproof · cited by 0
- MeasureTheory.Integrable.edist_toL1_zeroproof · cited by 0
- MeasureTheory.Integrable.enorm_toL1proof · cited by 0