isProbabilityMeasure — Mathlib

English

The zero kernel together with any CondKernel κCond forms a CondKernel: the disintegration is trivial.

Русский

Нуль-ядро вместе с любым κCond образуют CondKernel; разложение тривиально.

LaTeX

$$$IsCondKernel 0 \\; \\kappaCond$$$

Lean4

theorem isProbabilityMeasure [MeasurableSingletonClass α] {a : α} (ha : ρ.fst { a } ≠ 0) :
    IsProbabilityMeasure (ρCond a) := by
  constructor
  rw [IsCondKernel.apply_of_ne_zero _ _ ha, prod_univ, ← Measure.fst_apply (measurableSet_singleton _),
    ENNReal.inv_mul_cancel ha (measure_ne_top _ _)]

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