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Can a power series of several variables be discontinuous on a compact set if it converges in every point of this set?
Say we have a power series of two variables, with an associated function $f$ defined as
$$
\begin{split}
f(x, y) =\, & \sum_{n,m} a_{n,m}x^ny^m,\\
& a_{n,m} \geq 0 \quad \forall n, m \in\...
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