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3. Let Y be a random variable and Sy 0,1] (the closed unit interval) be its sample space. What is the o-algebra Fy generated by the open intervals 1(0, 1/2), (1/2,1)1? . If we define a probability measure y by only specifying its value on the above two open intervals (i.c., the two generators), say uy((0, 1/2)-1/3 and My((1/2, 1))-1/3, then can you complete the definition of : Fy 0,1] by extending it to the entire a-algebra Fy? Is the extension unique?

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