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**zebra2147** My professor did not discuss this topic in class but it came up in his notes. Any help would be appreciated.

He states that a function $\displaystyle f$ satisfies a Holder condition of order $\displaystyle \alpha$, if there are constants $\displaystyle \alpha >0$ and $\displaystyle M>0$, such that $\displaystyle |f(x)-f(y)|\leq M|x-y|^\alpha$ for all $\displaystyle x$ and $\displaystyle y$.

Now, if $\displaystyle f$ is Holder, prove that $\displaystyle f$ is uniformly continuous.