Theorems · Theorem · measure theory
MeasureTheory.Integrable.sub
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
{f g : α → β}, MeasureTheory.Integrable f μ → MeasureTheory.Integrable g μ → MeasureTheory.Integrable (f - g) μ- Cited by
- 36 results in Mathlib
- Foundations
- Depth 208 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.
Cites7
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
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- sub_eq_add_negproof · cited by 1,023
- MeasureTheory.Integrable.addproof · cited by 42
- MeasureTheory.Integrable.negproof · cited by 40
Cited by36
Results whose statement or proof uses this declaration.
- MeasureTheory.IntegrableOn.subproof · cited by 14
- MeasureTheory.SignedMeasure.integrable_rnDerivproof · cited by 9
- MeasureTheory.tendsto_setToFun_of_dominated_convergenceproof · cited by 5
- ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExpproof · cited by 3
- MeasureTheory.Submartingale.expected_stoppedValue_monoproof · cited by 3
- MeasureTheory.tendsto_of_integral_tendsto_of_monotoneproof · cited by 3
- MeasureTheory.tendsto_setToFun_of_L1proof · cited by 3
- MeasureTheory.martingale_martingalePartproof · cited by 2
- MeasureTheory.Submartingale.sum_smul_subproof · cited by 2
- MeasureTheory.exists_lt_lowerSemicontinuous_integral_ltproof · cited by 2
- MeasureTheory.VectorMeasure.Integrable.subproof · cited by 2
- MeasureTheory.submartingale_of_setIntegral_leproof · cited by 2