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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
0
votes
If $t \to \lVert f(\cdot,t) \rVert_{L^2_x}^2$ is absolutely continuous, can we interchange t...
I will not assume function $$\psi(t) := \lVert f(\cdot,t) \rVert_{L^2_x}^2$$ be absolutely continuous.
We have $f\in W^{1,q'}_t\bigl([0,\infty), L^{p'}_x(S^1)\bigr)$, so $f$ has a representative $\til …
10
votes
2
answers
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Absolute continuity on $R^{n}$
I know the definition of absolute continuity if there is a function $f:(a,b)\rightarrow R$.
I wonder what is an analogy of this concept if we have a function $f:A\rightarrow R$, where $A\subset R^{n}$ …