English
For a, a node in the universe, a ∈ (ofMultiset s hs).support iff a ∈ s.toFinset.
Русский
Для элемента a: a принадлежит поддержке ofMultiset s hs тогда и только тогда, когда a принадлежит s.toFinset.
LaTeX
$$$$ a \\in (\\mathrm{ofMultiset}(s, hs)).\\mathrm{support} \\; \\Longleftrightarrow \\; a \\in s^{\\mathrm{toFinset}} $$$$
Lean4
@[fun_prop]
theorem comp {𝒴 : Type*} {m𝒴 : MeasurableSpace 𝒴} {ν : Measure 𝒴} {Y : 𝓧 → 𝒴} (hY : HasLaw Y ν μ) (hX : HasLaw X μ P) :
HasLaw (Y ∘ X) ν P
where
aemeasurable := (hX.map_eq ▸ hY.aemeasurable).comp_aemeasurable hX.aemeasurable
map_eq := by
rw [← AEMeasurable.map_map_of_aemeasurable _ hX.aemeasurable, hX.map_eq, hY.map_eq]
rw [hX.map_eq]; exact hY.aemeasurable
