Theorems · Theorem · measure theory

MeasureTheory.lpMeasToLpTrimLie_symm_indicator

∀ {α : Type u_1} {F : Type u_2} {p : ENNReal} [inst : NormedAddCommGroup F] {m m0 : MeasurableSpace α}
  [one_le_p : Fact (1 ≤ p)] [inst_1 : NormedSpace ℝ F] {hm : m ≤ m0} {s : Set α} {μ : MeasureTheory.Measure α}
  (hs : MeasurableSet s) (hμs : (μ.trim hm) s ≠ ⊤) (c : F),
  ↑((MeasureTheory.lpMeasToLpTrimLie F ℝ p μ hm).symm (MeasureTheory.indicatorConstLp p hs hμs c)) =
    MeasureTheory.indicatorConstLp p ⋯ ⋯ c

When applying the inverse of lpMeasToLpTrimLie (which takes a function in the Lp space of the sub-sigma algebra and returns its version in the larger Lp space) to an indicator of the sub-sigma-algebra, we obtain an indicator in the Lp space of the larger sigma-algebra.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

2 results in Mathlib

Foundations

Depth 241 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupFactNormedSpace