# Tagged Questions

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### Justification of the convolution operation of $L^1(G)$ functions where $G$ is a LCA group (measurability)

Suppose $G$ is a locally compact abelian Hausdorff group (LCA), and $\lambda$ is the Haar measure on it. We all know the convolution of two $L^1(\lambda)$ functions $f$ and $g$ on $G$ is defined as ...
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### Entropy for Haar measure on $O(n)$

Let $G$ be a locally compact group. A measure $\mu$ is the right-Haar measure on $G$ if for every $g\in G$ and $E\subseteq G$ Borel set $\mu(Eg)=\mu(E)$. It is known that every locally compact group ...
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### Rate of convergence of the average of an equidistributed sequence

Let $f : \mathbb R\to\mathbb C$ be an $1$-periodic and sufficiently smooth function, which has zero average, and let $\alpha$ irrational. We know the following: a. ...
Let $f:\mathbb R\to\mathbb C$ be a sufficiently smooth and $1$-periodic function of average zero (i.e., $\int_0^{1}f(x)\,dx=0$), and let $\alpha\in(0,1)\smallsetminus\mathbb Q$. We know that $$... 0answers 84 views ### Differentiability of f*g on the circle, for integrable f, bounded g, and some decay of the Fourier coefficients of f If f\in L^1(\mathbb{T}) and g\in L^\infty(\mathbb{T}) where \mathbb{T} is the circle, such that \hat{f}\in L^{p}(\mathbb{Z}) for some 1\leq p<\infty, do we have that f*g is ... 0answers 123 views ### A problem concerning measures on locally compact spaces I am stuck on a question for quite sometime now, although in the text it is said to be "apparent". The problem goes as the following : Let X and Y be locally compact Hausdorff spaces. Then M(X) ... 1answer 353 views ### Pointwise limit at Lebesgue's point Dear MOs, I am sorry if this problem is too elementary for someone. I just want to get confirmation. Suppose f\in L^1(R^d). Since almost all points are Lebesgue points by the Lebesgue ... 0answers 365 views ### Measure Theoretic view of Hardy Littlewood Circle Method Is it possible to view the Hardy-Littlewood Circle method as the Fourier transform with respect to the Lebesgue measure on [0,1) for an appropriate generating function defined in terms of additive ... 1answer 384 views ### Ergodic decomposition of quasi-invariant measure I have a reference request concerning Proposition 1.6 in the following article http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183548783 The ... 1answer 443 views ### Measures and structure on conjugacy classes Given a locally compact group G, does there exist a measure \nu on the conjugacy classes conj(G) such that for f \in C_c(G)$$ \int_G f(g) d \mu_G(g) = \int_{conj(H)} \int_{G / G_\gamma} ...
Hi, Let $R$ be equipped with the usual Borel structure. Let $F$ be a Borel subset and $E$ be a closed subset of $R$. Then $F+E=(f+e: f\in F, e \in E \)$ is Borel? If yes, is it true for any locally ...