instIsProbabilityMeasure — Mathlib

English

If ρ is a probability measure, then its first marginal ρ.fst is also a probability measure.

Русский

Если ρ — вероятностьная мера, то ρ.fst также является вероятностной мерой.

LaTeX

$$$$\\text{If } ρ \\text{ is probability, then } ρ.fst \\text{ is probability.}$$$$

Lean4

instance instIsProbabilityMeasure [IsProbabilityMeasure ρ] : IsProbabilityMeasure ρ.fst where
  measure_univ := by
    rw [fst_univ]
    exact measure_univ

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