Determine at least 3 s-measurable functions

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Reference no: EM133018976

Question 1: Let X = (-5, 10]. Give atleast 3 σ-algebras on X. Provide proof or solution showing that each set contains the properties of a a-algebra on X.

Question 2: Define at least 5 sets A ⊂ R such that |A| = 5. Provide proof or solution showing that each set has outer measure 5.

Question 3. Suppose f: [0, 4Π] → R is defined by f (x) = cos x. Identify f^-1(A) for the following:

a. A = (0, ∞)
b. A = [0,1]
c. A = (1)
d. A = (2,3)

Question 4: Determine at least 3 S-measurable functions. Explain why these functions are S-measurable.

Reference no: EM133018976

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