Theorems · Theorem · functional analysis
MeasureTheory.MemLp.eLpNorm_lt_top
∀ {α : Type u_1} {ε : Type u_2} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} [inst : ENorm ε]
[inst_1 : TopologicalSpace ε] {f : α → ε}, MeasureTheory.MemLp f p μ → MeasureTheory.eLpNorm f p μ < ⊤- Cited by
- 10 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENormTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.eLpNormstatement · cited by 329
- ENormstatement and proof · cited by 155
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.smulproof · cited by 13
- MeasureTheory.Integrable.add_measureproof · cited by 6
- MeasureTheory.Integrable.measure_enorm_ge_lt_topproof · cited by 3
- MeasureTheory.MemLp.meas_ge_lt_top'_enormproof · cited by 2
- MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zeroproof · cited by 1
- MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_memLpproof · cited by 1
- MeasureTheory.MemLp.enormproof · cited by 1
- MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_innerproof · cited by 1
- MeasureTheory.eLpNorm_count_lt_top_of_ltproof · cited by 1
- MeasureTheory.Integrable.uniformIntegrable_condExpproof · cited by 1