Theorems · Definition · measure theory

MeasureTheory.Measure.FiniteSpanningSetsIn.prod

{α : Type u_1} →
  {β : Type u_2} →
    [inst : MeasurableSpace α] →
      [inst_1 : MeasurableSpace β] →
        {μ : MeasureTheory.Measure α} →
          {ν : MeasureTheory.Measure β} →
            {C : Set (Set α)} →
              {D : Set (Set β)} →
                μ.FiniteSpanningSetsIn C →
                  ν.FiniteSpanningSetsIn D → (μ.prod ν).FiniteSpanningSetsIn (Set.image2 (fun x1 x2 => x1 ×ˢ x2) C D)

μ.prod ν has finite spanning sets in rectangles of finite spanning sets.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

3 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace