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Exercise 1. Let = [0; 1] and F be the sigma-algebra generated by the dyadic intervals

[k/4,(k+1)/4]; k = 0; 1; 2; 3 :

(a) List all events in F.

(b) Let X be function defined on omega (I don't know how to type the greek letter) as follows:

X(w)={k/4 if k/4=< w < (k+1)/4 and w<1/2

1/2 if w>=1/2 }

where k = 0; 1; 2; 3. Show that X is F-measurable.

(c) Give an example of a function Z : omega-->R such that Z takes only finite number of values and is not F-measurable.

I guess once I've got the idea sorted..then I'll be able to understand more...