Theorems · Theorem · functional analysis
MeasureTheory.eLpNorm_norm
∀ {α : Type u_1} {F : Type u_5} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup F] (f : α → F), MeasureTheory.eLpNorm (fun x => ‖f x‖) p μ = MeasureTheory.eLpNorm f p μ- Cited by
- 5 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- 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
- Norm.normstatement · cited by 5,413
- Filter.Eventually.of_forallproof · cited by 526
- MeasureTheory.eLpNormstatement · cited by 329
- norm_normproof · cited by 113
- MeasureTheory.eLpNorm_congr_norm_aeproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNormproof · cited by 3
- MeasureTheory.SimpleFunc.memLp_approxOnproof · cited by 3
- MeasureTheory.lpNorm_normproof · cited by 2
- ProbabilityTheory.MemLp.uniformIntegrable_of_identDistrib_auxproof · cited by 1
- MeasureTheory.memLp_norm_iffproof · cited by 1