I am reading Rudin's proof (3rd edition) and am wondering what substitution is made to make it true that $P_n(x)=$ the integral from $-x$ to $1-x$ is equal to the same function integrated from -1 to 1. He says there's a substitution but I haven't found the right one. Thanks a lot
Stone-Weierstrass theorem proof (Rudin)
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real-analysis
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0I do not have Rudin's book right now, but I'd suggest an affine change of variable: $x \mapsto \alpha x + \beta$. – 2012-08-07