(Rudin, Ch. 6, Exercise 10) Let p and q be positive real numbers satisfying 1 1 +== 1. - Prove the following statements: (a) If u >0 and v > 0, then UP uv


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(Rudin, Ch. 6, Exercise 10) Let p and q be positive real numbers satisfying<br>1<br>1<br>+== 1.<br>-<br>Prove the following statements:<br>(a) If u >0 and v > 0, then<br>UP<br>uv <<br>+<br>Equality holds if and only if uP = vª.<br>(b) If ƒ E R(a), g€ R(a), f 2 0, g 2 0, and<br>fP da = 1 =<br>gª da,<br>a<br>then<br>| fg da < 1.<br>a<br>

Extracted text: (Rudin, Ch. 6, Exercise 10) Let p and q be positive real numbers satisfying 1 1 +== 1. - Prove the following statements: (a) If u >0 and v > 0, then UP uv < +="" equality="" holds="" if="" and="" only="" if="" up="vª." (b)="" if="" ƒ="" e="" r(a),="" g€="" r(a),="" f="" 2="" 0,="" g="" 2="" 0,="" and="" fp="" da="1" =="" gª="" da,="" a="" then="" |="" fg="" da="">< 1.="">

Jun 04, 2022
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