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Suppose $0<\mu (A)<\infty$ and $0<\mu (B)<\infty,$ and $A\cap B=\phi.$ (1).Let $f(x)=1/\mu (A)$ when $x\in A$ and $f(x)=0$ when $x\not \in A.$ Let $g(x)=1/\mu (B)$ when $x \in B$ and $g(x)=0$ when $x\not \in B.$ Then $f, g$ are linearly independent, and $\|(f+g)/2\|_1=\|f\|_1=\|g\|_1=1.$ (2). Let $f(x)=1$ when $x\in A$ and $f(x)=0$ when $x ...



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