@article{Deterding_2019, title={Bounded point derivations on $R^p(X)$ and approximate derivatives}, volume={124}, url={https://www.mscand.dk/article/view/109998}, DOI={10.7146/math.scand.a-109998}, abstractNote={<p>It is shown that if a point $x_0$ admits a bounded point derivation on $R^p(X)$, the closure of rational function with poles off $X$ in the $L^p(dA)$ norm, for $p >2$, then there is an approximate derivative at $x_0$. A similar result is proven for higher-order bounded point derivations. This extends a result of Wang which was proven for $R(X)$, the uniform closure of rational functions with poles off $X$.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Deterding, Stephen}, year={2019}, month={Jan.}, pages={132–148} }