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$u \in L^2(R^n)$

I am guessing that $L^2(R^n)$ means the $L^2$ norm over an n-dimensional vector. The context is an energy minimization function : total variation–based model of Rudin, Osher, and Fatemi (ROF)

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    It would be most helpful if you provide more context, yes.2011-06-03

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$L^2(\mathbb{R}^n)$ is the space of all measurable functions $f\colon \mathbb{R}^n \to \mathbb{R}$ (or possibly $f\colon \mathbb{R}^n \to \mathbb{C}$) such that $ \int_{\mathbb{R}^n} |f|^2 \;<\; \infty\text{,} $ where the integral is a Lebesgue integral. (The square root of this integral is the 2-norm of $f$.)

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    The best place (in my opinion) to learn about basic measure theory is Walter Rudin's book "Real and Complex Analysis". The first three chapters furnish a decent background in the subject. However, once you read the first three chapters, you will not be able to stop!2011-06-03