Theorems · Theorem · functional analysis
MeasureTheory.Lp.continuous_posPart
∀ {α : Type u_1} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} [inst : Fact (1 ≤ p)],
Continuous fun f => MeasureTheory.Lp.posPart f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- Continuousstatement · cited by 2,592
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- MeasureTheory.Lp.posPartstatement · cited by 8
- MeasureTheory.Lp.lipschitzWith_pos_partproof · cited by 3
- LipschitzWith.continuous_compLpproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.L1.integral_eq_norm_posPart_subproof · cited by 1
- MeasureTheory.Lp.continuous_negPartproof · cited by 1