Theorems · Theorem · measure theory
MeasureTheory.condExp_nonneg
∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → E}
[inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] [inst_3 : PartialOrder E]
[ClosedIciTopology E] [IsOrderedAddMonoid E] [IsOrderedModule ℝ E], 0 ≤ᵐ[μ] f → 0 ≤ᵐ[μ] μ[f | m]- Cited by
- 7 results in Mathlib
- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- PartialOrderstatement and proof · cited by 6,410
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.aestatement and proof · cited by 2,352
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- MeasureTheory.Integrableproof · cited by 1,367
- Filter.EventuallyLEstatement and proof · cited by 383
- MeasureTheory.condExpstatement and proof · cited by 234
Cited by7
Results whose statement or proof uses this declaration.
- Integrable.norm_condExp_rpow_leproof · cited by 3
- norm_condExp_leproof · cited by 2
- MeasureTheory.integral_condExp_le_of_ae_nonnegproof · cited by 2
- MeasureTheory.abs_condExp_ae_le_condExp_absproof · cited by 2
- MeasureTheory.condLExp_enormproof · cited by 1
- MeasureTheory.tendsto_sum_indicator_atTop_iffproof · cited by 1
- MeasureTheory.condLExp_ofRealproof · cited by 1