For every one dimensional set C, define the function Q(C) C f(x), where f(x) (2 3)(1 3) x , x 0, 1, 2, , zero elsewhere If C 1 x x 0, 1, 2, 3 and C 2 x x 0, 1, 2, , find Q(C 1 ) and Q(C 2 )

Question: For every one-dimensional set C, define the function Q(C) = C f(x), where f(x) = (2/3)(1/3) x , x = 0, 1, 2, .

For every one-dimensional set C, define the function Q(C) = Σ_C f(x), where f(x) = (2/3)(1/3)^x, x = 0, 1, 2, . . . , zero elsewhere. If C₁ = {x : x = 0, 1, 2, 3} and C₂ = {x : x = 0, 1, 2, . . .}, find Q(C₁) and Q(C₂).

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