Documentation

Mathlib.MeasureTheory.Function.LpSeminorm.Count

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 : αε) (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 : αε) (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 : αε} {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 : αε} {p : ENNReal} [Finite α] (hp : p 0) :
eLpNorm f p Measure.count < ∀ (i : α), f i‖ₑ <