volume_subtype_coe_eq_zero_of_volume_eq_zero

English

For measurable s, and μ, and t ⊆ s, the comap of μ along Subtype.val on t equals μ on the image of t.

Русский

Для измеримого s и μ и t ⊆ s, комап по Subtype.val на t равен μ на образе t.

LaTeX

$$$\mathrm{comap}(\mathrm{Subtype.val}, μ) \, t = μ((\mathrm{Subtype.val})'' t).$$$

Lean4

theorem volume_subtype_coe_eq_zero_of_volume_eq_zero (hu : NullMeasurableSet u) {t : Set u} (ht : volume t = 0) :
    volume (((↑) : u → δ) '' t) = 0 :=
  measure_subtype_coe_eq_zero_of_comap_eq_zero hu ht

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