toFilter — Mathlib

English

Monotonicity lemma for MemBaseSet under partial orders.

Русский

Лемма монотонности MemBaseSet при частичных упоряднениях.

LaTeX

$$$\\text{MemBaseSet}$ monotone with respect to $(l, c, r)$$$

Lean4

/-- A set `s : Set (TaggedPrepartition I)` belongs to `l.toFilter I` if for any `c : ℝ≥0` 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`. -/
def toFilter (l : IntegrationParams) (I : Box ι) : Filter (TaggedPrepartition I) :=
  ⨆ c : ℝ≥0, l.toFilterDistortion I c

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