Theorems · Theorem · functional analysis
MeasureTheory.nontrivial_Lp_real_of_nontrivial_Lp
∀ {α : Type u_1} (E : Type u_2) [inst : NormedAddCommGroup E] {mα : MeasurableSpace α} (p : ENNReal)
(μ : MeasureTheory.Measure α) [Nontrivial ↥(MeasureTheory.Lp E p μ)], Nontrivial ↥(MeasureTheory.Lp ℝ p μ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroupNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- 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.topproof · cited by 9,680
- Norm.normproof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- MeasurableSetproof · cited by 3,075
- one_mulproof · cited by 2,841
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.completeSpace_of_completeSpace_Lpproof · cited by 1