uniformOn_eq_zero — Mathlib

English

Under a measurable singleton assumption, uniformOn s = 0 iff s is infinite or empty.

Русский

При предположении измеримости самосущности множества, uniformOn s = 0 тогда, когда s бесконечно или пусто.

LaTeX

$$$\text{uniformOn}(s) = 0 \iff s\text{ бесконечно} \lor s = \varnothing$$$

Lean4

/-- See `uniformOn_eq_zero'` for a version assuming `MeasurableSet s` instead of
`MeasurableSingletonClass Ω`. -/
@[simp]
theorem uniformOn_eq_zero [MeasurableSingletonClass Ω] : uniformOn s = 0 ↔ s.Infinite ∨ s = ∅ := by simp [uniformOn]

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