Claims

../

2024_12_16_kovac_predojevic: Every measurable planar set of infinite measure contains the vertices of a cyclic quadrilateral of area one, while some planar set of infinite measure contains no convex polygon with congruent sides and area one.

2025_01_03_koizumi: Every planar measurable set of infinite measure contains the vertices of an isosceles trapezoid of area one, and every unbounded set of positive measure contains those of an isosceles triangle and of a right triangle of area one.

---