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the definition? This paragraph does not say explicitly. It does explain the scare-quoted L0 norm (or "norm"), but I think that this is almost always what is intended when the term L0 norm is used, even though it's not truly a norm. I was left more confused than before after reading this definition
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In the section on the space of measurable functions, there's a definition of a metric referred to as a Lévy metric without reference. Given that the Lévy metric usually refers to a very different metric, it'd be good to have a reference (from a preliminary search, I couldn't find even one).
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The mathematical definition of the ℓ0 norm was established by Banach's Theory of Linear
Operations. The space of sequences has a complete metric topology provided by the F-norm ...
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The definition of and L^p space should come right away, before applications. And where it is defined, it says they "may be defined as...", which sounds un-encyclopedic.
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Additionally, the metric given is equivalent to the Ky Fan metric, so it perhaps would seem more reasonable to just call it that. Either way, clarification is needed.
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I agree, I find this section lacking. I might update it a bit. Anyone have any additional comments about adding things or editing things to it?
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In the section "The p-norm in finite dimensions", subsection "Definition", the 2nd property is not quite correct. In the sentence "
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until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Regards,
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This page should include examples of functions which are contained in one L^p space, but not another. This
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until a consensus is reached, and readers of this page are welcome to contribute to the discussion.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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the length of the vector is positive homogeneous with respect to multiplication by a scalar
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I hope someone knowledgeable about this subject will fix this.
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before the subject of the article has even been defined
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Confusion with metric in section 6.1 -- needs reference
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there my be an error in the section about
Embeddings.
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to determine whether its use and function meets the
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