Theorems · Theorem · functional analysis
MeasureTheory.Lp.eLpNorm_ne_top
∀ {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)), MeasureTheory.eLpNorm (↑↑f) p μ ≠ ⊤- Cited by
- 20 results in Mathlib
- Foundations
- Depth 222 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
- Top.topstatement · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- LT.lt.neproof · cited by 872
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.eLpNormstatement · cited by 329
- MeasureTheory.Lp.eLpNorm_lt_topproof · cited by 2
Cited by20
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'proof · cited by 5
- MeasureTheory.Lp.enorm_defproof · cited by 4
- MeasureTheory.Lp.edist_distproof · cited by 2
- MeasureTheory.Lp.nnnorm_le_of_ae_boundproof · cited by 2
- MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonnegproof · cited by 1
- MeasureTheory.continuous_L1_toL1proof · cited by 1
- MeasureTheory.eLpNorm_condExpL2_leproof · cited by 1
- MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_topproof · cited by 1
- MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mulproof · cited by 1
- MeasureTheory.norm_condExpL2_coe_leproof · cited by 0
- MeasureTheory.Lp.meas_ge_le_mul_pow_enormproof · cited by 0
- MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNormproof · cited by 0