Question: All sets figuring below are subsets of the product space W 1 ´ W 2 . Then show that (i) E Ã F implies E

All sets figuring below are subsets of the product space W1´ W2. Then show that

(i) E Í F implies Ew1 Í Ew1 and Ew2 Ã Ew2, w1 ÃŽ W1, w2 ÃŽ, W2.

(ii) E Ç F Ø implies Ew1 Ã‡Ew1 = Ew2 Ã‡ Ew2 = Ø, w1 ÃŽ W1, w2 ÃŽ W2.

(iii) For n = 1, 2,€¦.

= U En,02 n = 1, 2, ..., (U En = U En,01, (U En 02

And in particular,

All sets figuring below are subsets of the product space

w2 ÃŽ W2.

(iv) For n = 1, 2,€¦.,

All sets figuring below are subsets of the product space

w2 ÃŽ W2.

(v) (Ec) w1 = (Ew1)c, (Ec) w2 = (Ew2)c, w1 ÃŽ W1, w2 ÃŽ W2.

= U En,02 n = 1, 2, ..., (U En = U En,01, (U En 02

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