Abstract
We define and investigate the class \(\tau _m^N(x)\) of functions provided with the notion of m-approximate Nth degree Taylor polynomial at \(x\in {\mathbb {R}}^n\). In particular we compare \(\tau _m^N(x)\) with the class \(t^{k,p}(x)\) of functions having the derivative of order k in the \(L^p\) sense at x (Ziemer in Weakly differentiable functions. GTM, Springer, Berlin, 1989, Section 3.5). We apply this machinery to prove several properties of Sobolev functions, such as a new sectional superdensity property.
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