Sumset Of Cantor Set

Probability Level 3

Let C+C\mathcal{C} + \mathcal{C} denote the sumset of the Cantor set C\mathcal{C}. That is, C+C={x+y:x,yC}.\mathcal{C} + \mathcal{C} = \{x+y \, : \, x, y \in \mathcal{C}\}. Which of the following statements is true about C+C\mathcal{C} + \mathcal{C}?

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