Is there some $c > 0$ such that every measurable $A \subseteq \mathbb{R}^2$ of measure $\geq c$ contains the vertices of a triangle of area 1?

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

1True ↔2  ∃ c > 0,3    ∀ (A : Set (EuclideanSpace ℝ (Fin 2))),4      MeasurableSet A →5        ↑(MeasureTheory.volume A) ≥ ↑c →6          ∃ t,7            (∀ (p : Fin 3), t.points p ∈ A) ∧ EuclideanGeometry.triangle_area (t.points 0) (t.points 1) (t.points 2) = 1

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