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Is there any other norms besides cut norm defined on graphon?

Let $\mathcal{W}$ denote the space of all bounded symmetric measurable functions $W : [0, 1]^2 \rightarrow \mathbb{R}.$ For any $W\in\mathcal{W}$ we say it is a kernel and define its cut norm $\lVert ...
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Locally uniformly convexity in kernels (generalized definition of graphon) with cut norm

Let $\mathcal{W}$ denote the space of all bounded symmetric measurable functions $W : [0, 1]^2 \rightarrow \mathbb{R}.$ For any $W\in\mathcal{W}$ we say it is a kernel and define its cut norm $\lVert ...