L^p-seminorms on count and dirac #
@[simp]
theorem
MeasureTheory.eLpNorm_dirac
{α : Type u_1}
{ε : Type u_2}
[MeasurableSpace α]
[MeasurableSingletonClass α]
[TopologicalSpace ε]
[ContinuousENorm ε]
{p : ENNReal}
(f : α → ε)
(i : α)
(hp : p ≠ 0)
:
theorem
MeasureTheory.enorm_le_eLpNorm_count
{α : Type u_1}
{ε : Type u_2}
[MeasurableSpace α]
[MeasurableSingletonClass α]
[TopologicalSpace ε]
[ContinuousENorm ε]
{p : ENNReal}
(f : α → ε)
(i : α)
(hp : p ≠ 0)
:
theorem
MeasureTheory.eLpNorm_count_lt_top_of_lt
{α : Type u_1}
{ε : Type u_2}
[MeasurableSpace α]
[MeasurableSingletonClass α]
[TopologicalSpace ε]
[ContinuousENorm ε]
{f : α → ε}
{p : ENNReal}
[Finite α]
(h : ∀ (i : α), ‖f i‖ₑ < ⊤)
:
theorem
MeasureTheory.eLpNorm_count_lt_top
{α : Type u_1}
{ε : Type u_2}
[MeasurableSpace α]
[MeasurableSingletonClass α]
[TopologicalSpace ε]
[ContinuousENorm ε]
{f : α → ε}
{p : ENNReal}
[Finite α]
(hp : p ≠ 0)
: