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Jan
19
asked Different definitions for Lebesgue points
Jan
16
comment How to define the derivative of Radon measures
Of course, the for all quantifier in that case is to be regarded as "for all $r$ sufficiently small$. As the measure is positive, there is either a $\mu$-negligible ball or not.
Jan
14
comment How to define the derivative of Radon measures
$\bar{B_r(x)}$ denotes just the closure \bar{B_r(x)}. Corrected, didn't know how to do until now.
Jan
14
revised How to define the derivative of Radon measures
corrected tex
Jan
14
comment How to define the derivative of Radon measures
Compare the Frechet-derivative or Gateaux-derivative. Of course, the question of convergence of the difference quotient is more subtle in the infinite-dimensional case.
Jan
14
revised How to define the derivative of Radon measures
added 16 characters in body
Jan
14
awarded  Critic
Jan
14
comment Arbitrary non-integer power of a matrix
Does the square root of a matrix defined with this approach coincide with the canoical square root $\sqrt(A^\ast A )$?
Jan
14
accepted Intuition for not-so-smooth manifolds
Jan
14
accepted Finest topology on a space of banach space operators
Jan
14
accepted Arbitrary non-integer power of a matrix
Jan
13
asked How to define the derivative of Radon measures
Jan
8
asked Arbitrary non-integer power of a matrix
Dec
22
comment Finest topology on a space of banach space operators
yes, that's it. Further rewritten.
Dec
22
revised Finest topology on a space of banach space operators
edited body
Dec
22
comment Finest topology on a space of banach space operators
Thanks, i clarified this.
Dec
22
asked Finest topology on a space of banach space operators
Dec
17
comment Dual of Sobolev space $W^{1,p}(U)$ for $U$ an arbitrary subset of $\mathbb R^n$
Let $X$ be the (closed) image of the embedding into $Z = L^p \times (L^p)^n$ as described by you. Let $Y$ be the subspace of $Z'$ that vanishes on $X$. Then $X' \equiv Z'/Y$. We have $Z' = L^q \times (L^q)^n$. How do you employ the Hahn-Banach theorem?
Dec
17
asked Intuition for not-so-smooth manifolds
Dec
16
comment Dual of Sobolev space $W^{1,p}(U)$ for $U$ an arbitrary subset of $\mathbb R^n$
You are right. $W^{1,p'} \subset (W^{1,p})'$, whilst for cases of sufficient regularity, as in case $p > n$ by Morrey's lemma, the dirac delta is already a continuous dual vector. However, I find it hard to give the space $(W^{1,p}(\mathbb R^n))'$ a 'nice' characterization.