$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Content Zero Condition

Let $S\subseteq\mathbb{R}^n$ be a nonempty and bounded set. $S$ has content zero if and only if for all $\epsilon >0$, there exists a finite set of boxes $\{I_i\subseteq\mathbb{R}^n:1\leq i\leq m\}$ such that $$\begin{align*} S\subseteq \bigcup_{i=1}^m I_i \end{align*}$$ and $$\begin{align*} \sum_{i=1}^{m}\mu(I_i)<\epsilon \end{align*}$$

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Content Zero Condition

Let $S\subseteq\mathbb{R}^n$ be a nonempty and bounded set. $S$ has content zero if and only if for all $\epsilon >0$, there exists a finite set of boxes $\{I_i\subseteq\mathbb{R}^n:1\leq i\leq m\}$ such that $$\begin{align*} S\subseteq \bigcup_{i=1}^m I_i \end{align*}$$ and $$\begin{align*} \sum_{i=1}^{m}\mu(I_i)<\epsilon \end{align*}$$

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FullPage
result
concepts
hypothesis
implications
proof

Content Zero Condition

Let $S\subseteq\mathbb{R}^n$ be a nonempty and bounded set. $S$ has content zero if and only if for all $\epsilon >0$, there exists a finite set of boxes $\{I_i\subseteq\mathbb{R}^n:1\leq i\leq m\}$ such that $$\begin{align*} S\subseteq \bigcup_{i=1}^m I_i \end{align*}$$ and $$\begin{align*} \sum_{i=1}^{m}\mu(I_i)<\epsilon \end{align*}$$

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Hypothesis

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Proof

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Content Zero Condition

Let $S\subseteq\mathbb{R}^n$ be a nonempty and bounded set. $S$ has content zero if and only if for all $\epsilon >0$, there exists a finite set of boxes $\{I_i\subseteq\mathbb{R}^n:1\leq i\leq m\}$ such that $$\begin{align*} S\subseteq \bigcup_{i=1}^m I_i \end{align*}$$ and $$\begin{align*} \sum_{i=1}^{m}\mu(I_i)<\epsilon \end{align*}$$

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Hypothesis

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Proof

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result
concepts
hypothesis
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proof