Questions tagged [lp-spaces]

For questions about $L^p$ spaces, that is, given a measure space $(X,\mathcal F,\mu)$, the vector space of equivalence class of measurable functions with $p$-th power of the absolute value integrable. Question can be about properties of elements of these spaces, or when the ambient space on a problem is a $L^p$ space.

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Show that if the integral of function with compact support on straight line is zero, then $f$ is zero almost everywhere

I want to prove that that given $f:R^2 \rightarrow R$ which is continuous with compact support s.t the integral of $f$ for every straight line $l$ is zero ($\int f(l(t))\mathrm{d}t=0$) then $f$ is ...