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jirilebl committed Dec 18, 2020
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Ji{\v r}\'i Lebl\\[3ex]}
\today
\\
(version 1.0)
(version 1.1)
\end{minipage}}

%\addtolength{\textwidth}{\centeroffset}
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\end{thm}

The hypotheses on $f$ and $\frac{\partial f}{\partial y}$ can be
weakened to some degree, see e.g.\ \exerciseref{exercise:strongerleibniz}.
weakened to a degree, see e.g.\ \exerciseref{exercise:strongerleibniz}.
The proof below requires that
$\frac{\partial f}{\partial y}$ exists and is continuous
as a function of two variables, and the $x$ interval must be the entire
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\lim_{t \downarrow a} f(t) \quad \Bigl( = \lim_{\substack{t \to a\\t > a}} f(t)
\Bigr) ,
\end{equation*}
as these seemed clearer in some of the situations in this book.
as these seemed the clearer option in some of the situations in this book.
We may write $\{ x_n \}$ for a sequence $\{x_n\}_{n=1}^\infty$ and similarly
$\lim x_n$ instead of $\lim_{n\to \infty} x_n$ when it is clear that $n$ is
the index of the sequence.
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