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Anthony Berg
2025-03-13 13:03:52 +01:00
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content/Definitions/Measure Theory/Hölder's Inequality.md Normal file
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$\| f \times g \|_{1} \leq \| f \|_{p} \times \| g \|_{q}$

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content/Definitions/Measure Theory/Minkowski's Inequality.md Normal file
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$\| f + g \|_{p} \leq \| f \|_{p} + \| g \|_{p}$

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content/Definitions/Measure Theory/Sigma-Algebra/Borel Sets.md
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# Definition
The $\sigma$[[Sigma-Algebra|-algebra]] generated by the [[Open Sets|open sets]] in a [[Topological Space|topological space]] $X$ is the $\sigma$[[Sigma-Algebra|-algebra]] of **Borel Sets** of $X$.
The $\sigma$[[Sigma-Algebra|-algebra]] generated by the [[Open Sets|open sets]] in a [[Topological Space|topological space]] $X$ is the $\sigma$[[Sigma-Algebra|-algebra]] of **Borel Sets** of $X$.

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content/Definitions/Measure Theory/Sigma-Algebra/Borel Sigma-Algebra.md
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# Definition
**Borel $\sigma$-algebra** on a [[Topological Space|topological space]] $X$ is the one generated by the [[Open Sets|open sets]] $\tau$.
**Borel $\sigma$-algebra** on a [[Topological Space|topological space]] $X$ is the one generated by the [[Open Sets|open sets]] $\tau$.