2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y)...

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2. Let E CRn+m. For every x ER, let Ex := {y € R™ st. (,y) € E}. Let fel(E). Proved that • for a.e. 2 ER, the function Ex

This is a slightly stronger version of the Fubinis Theorem that we proved in class, for instance one could define fxs and us

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ame belong to L (Ex) As foxe E L CIRM) And now ne (x,84)€ En * $ (ayo = kto the lof. f(294) • 2¢120,9). the f x EIR? f f(x,y This we get SSf=5(Sfon,y) dy) da Rn Exe

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2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y)...

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2. Let f : A ! B. DeÖne a relation R on A by xRy i§ f (x) = f (y). a. Prove that R is an equivalence relation on A. b. Let Ex = fy 2 A : xRyg be the equivalence class of x 2 A. DeÖne E = fEx : x 2 Ag...

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2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y)...

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Add Answer to: 2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y)...

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2. Let f : A ! B. DeÖne a relation R on A by xRy i§ f (x) = f (y). a. Prove that R is an equivalence relation on A. b. Let Ex = fy 2 A : xRyg be the equivalence class of x 2 A. DeÖne E = fEx : x 2 Ag...

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