Theorems · Theorem · functional analysis
MeasureTheory.Lp.coeFn_sub
∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] (f g : ↥(MeasureTheory.Lp E p μ)), ↑↑(f - g) =ᵐ[μ] ↑↑f - ↑↑g- Cited by
- 13 results in Mathlib
- Foundations
- Depth 221 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.
Cites11
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.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.AEEqFun.coeFn_subproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'proof · cited by 5
- MeasureTheory.integral_condExpL2_eqproof · cited by 3
- MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'proof · cited by 2
- MeasureTheory.Lp.edist_distproof · cited by 2
- MeasureTheory.continuous_L1_toL1proof · cited by 1
- LipschitzWith.norm_compLp_sub_leproof · cited by 1
- MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm''proof · cited by 0
- MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNormproof · cited by 0
- MeasureTheory.Lp.simpleFunc.sub_toSimpleFuncproof · cited by 0
- MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNormproof · cited by 0
- MeasureTheory.L1.dist_eq_integral_distproof · cited by 0
- MeasureTheory.L1.norm_sub_eq_lintegralproof · cited by 0