Theorems · Theorem · measure theory
MeasureTheory.Integrable.sup
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_8} [inst : NormedAddCommGroup β]
[inst_1 : Lattice β] [HasSolidNorm β] [IsOrderedAddMonoid β] {f g : α → β},
MeasureTheory.Integrable f μ → MeasureTheory.Integrable g μ → MeasureTheory.Integrable (f ⊔ g) μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- Latticestatement and proof · cited by 916
- MeasureTheory.memLp_one_iff_integrableproof · cited by 73
- HasSolidNormstatement and proof · cited by 67
- MeasureTheory.MemLp.supproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.supproof · cited by 1
- MeasureTheory.eLpNorm_one_le_of_leproof · cited by 1