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Let $I\subseteq\mathbb{R}^n$ be a box, $P$ a partition of $I$, $J$ the indexing set of $P$, and let $f:I\to\mathbb{R}$ be a function. For each $\vec{\alpha}\in J$, choose a point $\vec{x}^{\vec{\alpha}}\in I^{(\vec{\alpha})}$. We define the Riemann sum of $f$ with respect to the partition $P$ as
$$\begin{align*}
S(f, P):=\sum_{\vec{\alpha}\in J}f(\vec{x}^{(\vec{\alpha})})\mu(I^{(\vec{\alpha})})
\end{align*}$$
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Let $I\subseteq\mathbb{R}^n$ be a box, $P$ a partition of $I$, $J$ the indexing set of $P$, and let $f:I\to\mathbb{R}$ be a function. For each $\vec{\alpha}\in J$, choose a point $\vec{x}^{\vec{\alpha}}\in I^{(\vec{\alpha})}$. We define the Riemann sum of $f$ with respect to the partition $P$ as
$$\begin{align*}
S(f, P):=\sum_{\vec{\alpha}\in J}f(\vec{x}^{(\vec{\alpha})})\mu(I^{(\vec{\alpha})})
\end{align*}$$
Concepts
Coming soonUsed In
Coming soonHypothesis
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definition
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