Theorems · Theorem · functional analysis
MeasureTheory.Integrable.coeFn_toL1
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
{f : α → β} (hf : MeasureTheory.Integrable f μ), ↑↑(MeasureTheory.Integrable.toL1 f hf) =ᵐ[μ] f- Cited by
- 11 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.
Cites13
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 · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.Integrable.toL1statement · cited by 58
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.tendsto_setToFun_of_dominated_convergenceproof · cited by 5
- MeasureTheory.setToFun_congr_measure_of_integrableproof · cited by 5
- MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMulproof · cited by 5
- MeasureTheory.aestronglyMeasurable_condExpL1proof · cited by 5
- MeasureTheory.tendsto_setToFun_of_L1proof · cited by 3
- MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_partproof · cited by 2
- MeasureTheory.continuous_L1_toL1proof · cited by 1
- MeasureTheory.condExpL1_of_aestronglyMeasurable'proof · cited by 1
- MeasureTheory.setToFun_toL1proof · cited by 1
- MeasureTheory.setIntegral_condExpL1proof · cited by 1
- MeasureTheory.L1.norm_of_fun_eq_integral_normproof · cited by 0