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Title: Minkowski Inequality
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Series: Functional Analysis
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Chapter: Core Results in Functional Analysis
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YouTube-Title: Functional Analysis 20 | Minkowski Inequality
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Original video for YT-Members (dark): Watch on YouTube
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: fa20_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps
00:00 Introduction
01:00 Proof
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Subtitle in English (n/a)
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Quiz Content
Q1: What is the Minkowski’s inequality in $\ell^p(\mathbb{N})$?
A1: $ | x + y |_p \leq | x |_p + | y |_p $
A2: $ | x + y |_p \leq | x |_p^2 + | y |_p^2 $
A3: $ | x y |_p \leq | x |_p^2 + | y |_p^2 $
A4: $ | x - y |^2_p \leq | x |_p^2 + | y |_p^2 $
A5: $ | x \cdot y |_p \leq | x |_p + | y |_p $
Q2: What do we use the proof Minkowski’s inequality?
A1: We use Hölder’s inequality.
A2: We use that $\ell^p(\mathbb{N})$ is a Banach space.
A3: We use that $\ell^2(\mathbb{N})$ is a Hilbert space.
A4: We use the triangle inequality in $\ell^2(\mathbb{N})$.
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Last update: 2025-09
