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### Probability that a random projection doesn't reduce the distance of a point from a subspace too much

Consider the natural uniform measure (is it called the Haar measure?) on the set of $(n-k)$-dimensional subspaces of $R^n$. We are given a $d$-dimensional affine subspace $U$ (think of $d, k \ll n$; ...
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### Combining microlocal Helgason's support and Holmgren's theorem to prove injectivity of limited-angle Radon transform

This questions is slightly related to Kashiwara's watermelon theorem and Microlocal version of Helgason's (support) and Holmgren's theorems, in which I asked for some references. Now I ...
For $u \in \mathbb{S}^{d-1} \subset \mathbb{R}^d$, it is easy to show that: u=c_d \int_{\mathbb{S^{d-1}}} \xi \mathbb{1}_{\left\{x \cdot u >0 \right\}}(\xi) \ \rm{d}\sigma_{d-1}(\...
In the book of Helgason which is called "Radon transform and integral geometry", he defines on page 2 the Radon transform on hyperplanes as: $$\hat{f}(\xi) = \int_{\xi} f(x) dm(x)$$ Where $dm(x)$ ...