instMeasurableSpace — Mathlib

English

For probability measures μ and ν, the swap map yields (μ.prod ν).map Prod.swap = ν.prod μ.

Русский

Для вероятностных мер μ и ν перестановка факторов даёт (μ.prod ν).map Prod.swap = ν.prod μ.

LaTeX

$$$ (\mu \mathrm{prod} \nu) \mathrm{map} \mathrm{Prod.swap} = \nu \mathrm{prod} \mu $$$

Lean4

/-- Measurability structure on `Measure`: Measures are measurable w.r.t. all projections -/
instance instMeasurableSpace : MeasurableSpace (Measure α) :=
  ⨆ (s : Set α) (_ : MeasurableSet s), (borel ℝ≥0∞).comap fun μ => μ s

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