1. Suppose that = [0,1] and > 0. Let P({x}) = for all x [0,1]. Prove or disprove that P() is a probability measure of .

2. Let = [0,2] and suppose that P({0}) = P({2}) = 1 4 while P(A) equals (the length of A) divided by plus 1 4 if 0 A plus 1 4 if 2 A. Determine the such that P() satisfies the conditions of a probability measure of .

3. Show that in general, P(Ai) = P(Ai) does not hold.

4. Show that if A B, then P(A) P(B).

1. Suppose that =[0,1] and >0. Let P({x})= for all x[0,1]. Prove or disprove that P() is a probability measure of . 2. Let =[0,2] and suppose that P({0})=P({2})=41 while P(A) equals (the length of A ) divided by plus 41 if 0A plus 41 if 2A. Determine the such that P() satisfies the conditions of a probability measure of . 3. Show that in general, P(Ai)=P(Ai) does not hold. 4. Show that if AB, then P(A)P(B) 1. Suppose that =[0,1] and >0. Let P({x})= for all x[0,1]. Prove or disprove that P() is a probability measure of . 2. Let =[0,2] and suppose that P({0})=P({2})=41 while P(A) equals (the length of A ) divided by plus 41 if 0A plus 41 if 2A. Determine the such that P() satisfies the conditions of a probability measure of . 3. Show that in general, P(Ai)=P(Ai) does not hold. 4. Show that if AB, then P(A)P(B)