toFilterDistortioniUnion — Mathlib

English

Equivalences showing how toFilter_inf aligns with iUnion-based constructions.

Русский

Эквивалентности показывают, как toFilter_inf согласуется с конструкциями через iUnion.

LaTeX

$$$\\text{theorem toFilter_inf_iUnion_eq}$$$

Lean4

/-- A set `s : Set (TaggedPrepartition I)` belongs to `l.toFilterDistortioniUnion I c π₀` if
there exists a function `r : ℝⁿ → (0, ∞)` (or a constant `r` if `l.bRiemann = true`) such that `s`
contains each prepartition `π` such that `l.MemBaseSet I c r π` and `π.iUnion = π₀.iUnion`. -/
def toFilterDistortioniUnion (l : IntegrationParams) (I : Box ι) (c : ℝ≥0) (π₀ : Prepartition I) :=
  l.toFilterDistortion I c ⊓ 𝓟 {π | π.iUnion = π₀.iUnion}

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