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$\begingroup$

my question is probably rather simple I just never came across this notation:

$sup\{||f-f(\bullet-y)||: f\in K\}\rightarrow 0$ and I cannot realy seem to find what it indicates. I am guessing it means something in the sense of

$sup\{||g||: g(x)=(f(x)-f(x-y)) \forall x; f\in K||\}\rightarrow 0$

Does anybody know this notation and can verify or clarify this for me? If it makes a difference: The notation came across while looking into Sobolev Spaces.

Thankyou very much!

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    for $y\rightarrow 0$? – 2017-01-16
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    yes, sorry, forgot about that. I am mainly wondering about the $\bullet$... – 2017-01-16
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    Indeed the function $g=f-f(\cdot-y)$ is defined by $g(x)=f(x)-f(x-y)$ for every suitable $x$. Is this your question? – 2017-01-16
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    That was exactly my question! Thank you! – 2017-01-16

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