instIsOpenPosMeasureProdVolumeOfSFinite

English

If ν has no atoms, then μ × ν has no atoms (reiteration of the second-coordinate case).

Русский

Если ν не имеет атомов, то μ × ν не имеет атомов (повторение для второй координаты).

LaTeX

$$Same as NoAtoms snd$$

Lean4

instance {X Y : Type*} [TopologicalSpace X] [MeasureSpace X] [IsOpenPosMeasure (volume : Measure X)]
    [TopologicalSpace Y] [MeasureSpace Y] [IsOpenPosMeasure (volume : Measure Y)] [SFinite (volume : Measure Y)] :
    IsOpenPosMeasure (volume : Measure (X × Y)) :=
  prod.instIsOpenPosMeasure

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