Theorems · Theorem · functional analysis
MeasureTheory.Lp.aestronglyMeasurable
∀ {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.AEStronglyMeasurable (↑↑f) μ- Cited by
- 18 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.
Cites10
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
- MeasureTheory.AEStronglyMeasurablestatement · cited by 755
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.AEEqFun.aestronglyMeasurableproof · cited by 26
Cited by18
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.memLpproof · cited by 35
- MeasureTheory.L1.norm_eq_integral_normproof · cited by 3
- MeasureTheory.integrable_condExpIndSMulproof · cited by 2
- MeasureTheory.L2.integrable_innerproof · cited by 2
- MeasureTheory.integrable_condExpL2_indicatorproof · cited by 1
- MeasureTheory.L2.eLpNorm_inner_lt_topproof · cited by 1
- MeasureTheory.Lp.nnnorm_eq_zero_iffproof · cited by 1
- MeasureTheory.L2.mem_L1_innerstatement and proof · cited by 1
- MeasureTheory.tendstoInMeasure_of_tendsto_Lpproof · cited by 1
- MeasureTheory.mem_lpMeasSubgroup_toLp_of_trimproof · cited by 0
- MeasureTheory.Lp.meas_ge_le_mul_pow_enormproof · cited by 0
- MeasureTheory.mem_lpMeas_selfproof · cited by 0