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## fa.functional analysis – Continuity of Radon transform w.r.t the angle

let $f \in L^1(\mathbb R^n)$ (or in case it helps, actually a probability density on $\mathbb R^n$). fix $b \in \mathbb R$ and define the Radon transform $R[f]:S_{n-1} \times \mathbb R \to \mathbb R$ of $f$ by

$$R[f](w,b) := \int_{\mathbb R^n}\delta(x^\top w – b)f(x)\,dx, $$

where $S_{n-1}$ is the unit-sphere in $\mathbb R^n$.

**question.** *Under what minimal additional conditions on $f$ is mapping $w \mapsto R[f](w,b)$ continuous continuous on $S_{n-1}$for each $b \in \mathbb R$ ?*

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