Ben Green's Open Problem 3

Reference: [Ben Green's Open Problem 3](https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#section.3 Problem 3)

theorem Green3.green_3 : sorry ↔ ∀ (A : Set ℝ), IsOpen A → A ⊆ Set.Icc 0 1 → MeasureTheory.volume A > 1 / 3 → ∃ (x : ℝ) (y : ℝ) (z : ℝ), x ∈ A ∧ y ∈ A ∧ z ∈ A ∧ x * y = z

Suppose that $A \subset [0,1]$ is open and has measure greater than $\frac{1}{3}$. Is there a solution to $xy = z$ with $x, y, z \in A$?