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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*}

Concepts

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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*}

Concepts

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Hypothesis

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Results

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Proof

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FullPage
result
concepts
hypothesis
implications
proof
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*}

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon

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*}

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof