Theorems · Theorem · functional analysis
MeasureTheory.Lp.antitone
∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
[MeasureTheory.IsFiniteMeasure μ] {p q : ENNReal}, p ≤ q → MeasureTheory.Lp E q μ ≤ MeasureTheory.Lp E p μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- ENNRealstatement and proof · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.aestronglyMeasurableproof · cited by 26
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
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