measureOfNegatives — Mathlib

English

The set measureOfNegatives(s) consists of all real numbers that are the measures of measurable sets B with s ≤[B] 0.

Русский

Множество measureOfNegatives(s) состоит из всех чисел, равных значениям меры для_measureable множеств B с условием s ≤[B] 0.

LaTeX

$$$\\mathrm{measureOfNegatives}(s) = s''\\{B \\mid \\text{MeasurableSet } B \\land s \\le[B] 0\\}$$$

Lean4

/-- The set of measures of the set of measurable negative sets. -/
def measureOfNegatives (s : SignedMeasure α) : Set ℝ :=
  s '' {B | MeasurableSet B ∧ s ≤[B] 0}

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