S Let i Fi , i D 1 2, be two event spaces and 1 2 1 Show the following For every A 2 F1F2, the 1 section A 1 WD 2 2 2 W 1 2 2 A of A belongs to F2, and if f is a random variable on 1 2 F1 F2 then the function f 1 is a random variable on 2 F2

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Question: S Let . i ;Fi /, i D 1; 2, be two event spaces and !1 2 1. Show the following. For every A 2

S Let . i ;Fi /, i D 1; 2, be two event spaces and !1 2 1. Show the following. For every A 2 F1˝F2, the ‘!1-section’ A!1 WD ¹!2 2 2 W .!1; !2/ 2 Aº of A belongs to F2, and if f is a random variable on . 1 2;F1 ˝F2/ then the function f .!1; / is a random variable on . 2;F2/.

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