Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_count_lt_top

∀ {α : Type u_1} {ε : Type u_2} [inst : MeasurableSpace α] [MeasurableSingletonClass α] [inst_2 : TopologicalSpace ε]
  [inst_3 : ContinuousENorm ε] {f : α → ε} {p : ENNReal} [Finite α],
  p ≠ 0 → (MeasureTheory.eLpNorm f p MeasureTheory.Measure.count < ⊤ ↔ ∀ (i : α), ‖f i‖ₑ < ⊤)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Count

Cited by

0 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSingletonClassTopologicalSpaceContinuousENormFinite