field — Mathlib

English

The trimmed density μ.withDensityᵥ f, under a refinement of the measurable structure, remains absolutely continuous with respect to the trimmed measure's ENNReal-vector measure.

Русский

Обрезанная плотность μ.withDensityᵥ f сохраняет абсолютную непрерывность по отношению к обрезанной ENNReal-векторной мере.

LaTeX

$$$((\mu.withDensityᵥ f).trim hm) \ll^{\vee} (\mu.trim hm).toENNRealVectorMeasure$$$

Lean4

/-- The first-order theory of fields, as a theory over the language of rings -/
def _root_.FirstOrder.Language.Theory.field : Language.ring.Theory :=
  Set.range FieldAxiom.toSentence

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