Theorems · Theorem · measure theory

MeasureTheory.L1.norm_integral_le

∀ {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‖ ≤ ‖f‖

Defined in: Mathlib.MeasureTheory.Integral.Bochner.L1
Cited by: 1 results in Mathlib
Foundations: Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace CompleteSpace

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
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
Norm.normstatement and proof · cited by 5,413
AddSubgroupstatement · cited by 3,232
one_mulproof · cited by 2,841
CompleteSpacestatement and proof · cited by 2,532
MeasureTheory.AEEqFunstatement and proof · cited by 856

Cited by1

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MeasureTheory.L1.nnnorm_integral_leproof · cited by 0