restrict — Mathlib

English

Restricting a measure to a subset s yields the restricted measure μ|s, defined by μ|s(t) = μ(t ∩ s) for measurable t (and extended to all t).

Русский

Ограничение меры μ по подмножеству s даёт ограниченную меру μ|s, заданную на измеримых t как μ|s(t) = μ(t ∩ s).

LaTeX

$$$\mu\restriction s(t) = \mu(t \cap s) \quad \text{for all measurable } t.$$$

Lean4

/-- Restrict a measure `μ` to a set `s`. -/
noncomputable def restrict {_m0 : MeasurableSpace α} (μ : Measure α) (s : Set α) : Measure α :=
  restrictₗ s μ

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