Theorems · Theorem · measure theory
MeasureTheory.L1.integral_neg
∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
[inst_1 : NormedSpace ℝ E] [inst_2 : CompleteSpace E] (f : ↥(MeasureTheory.Lp E 1 μ)),
MeasureTheory.L1.integral (-f) = -MeasureTheory.L1.integral f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- ENNRealstatement · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- map_negproof · cited by 378
- MeasureTheory.L1.integralstatement · cited by 27
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