Theorems · Definition · functional analysis

MeasureTheory.Lp.compMeasurePreserving

{α : Type u_1} →
  {E : Type u_4} →
    {m : MeasurableSpace α} →
      {p : ENNReal} →
        {μ : MeasureTheory.Measure α} →
          [inst : NormedAddCommGroup E] →
            {β : Type u_7} →
              [inst_1 : MeasurableSpace β] →
                {μb : MeasureTheory.Measure β} →
                  (f : α → β) →
                    MeasureTheory.MeasurePreserving f μ μb → ↥(MeasureTheory.Lp E p μb) →+ ↥(MeasureTheory.Lp E p μ)

Composition of an L^p function with a measure-preserving function is an L^p function.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

19 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpace