Theorems · Theorem · measure theory

MeasureTheory.lpMeasSubgroupToLpTrim_norm_map

∀ {α : Type u_1} {F : Type u_2} {p : ENNReal} [inst : NormedAddCommGroup F] {m m0 : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} [hp : Fact (1 ≤ p)] (hm : m ≤ m0) (f : ↥(MeasureTheory.lpMeasSubgroup F m p μ)),
  ‖MeasureTheory.lpMeasSubgroupToLpTrim F p μ hm f‖ = ‖f‖

lpMeasSubgroupToLpTrim preserves the norm.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

1 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupFact