Theorems · Theorem · measure theory
MeasureTheory.L1.integral_eq_norm_posPart_sub
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (f : ↥(MeasureTheory.Lp ℝ 1 μ)),
MeasureTheory.L1.integral f = ‖MeasureTheory.Lp.posPart f‖ - ‖MeasureTheory.Lp.negPart f‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 248 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- Continuousproof · cited by 2,592
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- Continuous.compproof · cited by 371
- MeasureTheory.Lp.simpleFuncproof · cited by 122
- isClosed_eqproof · cited by 71
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_partproof · cited by 2