MutuallySingular — Mathlib

English

A reformulated variant asserting the same pi_lambda result in a structured form.

Русский

Переформулированный вариант утверждает тот же результат pi_lambda в структурированной форме.

LaTeX

$$$\text{AEMeasurable}\ f\mu \rightarrow \forall a, \text{AEMeasurable}(\lambda c. f c a)\mu$$$

Lean4

/-- Two measures `μ`, `ν` are said to be mutually singular if there exists a measurable set `s`
such that `μ s = 0` and `ν sᶜ = 0`. -/
def MutuallySingular {_ : MeasurableSpace α} (μ ν : Measure α) : Prop :=
  ∃ s : Set α, MeasurableSet s ∧ μ s = 0 ∧ ν sᶜ = 0

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