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>mfw realizing functions from [math] \mathbb{R} \to \mathbb{R} [/math] are just uncountably-infinite dimensional vectors
>integrals are just a way to sum uncountably many values that are zero
>because we have a norm on an [math]L^p[/math] space, we can define a topology, and given the topology we can make a Borel [math]\sigma[/math]-algebra on [math] L^p [/math] creating the measurable space [math](L^p(S), \mathcal{B}(L^p(S))[/math]
>on this space we can create a new [math]L^p[/math]-space
>we can continue in this manner until we have any number of embedded [math]L^p[/math]-spaces
>mfw realizing all this
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Bump brainlets
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Yes but this is all basic analysis
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>>8811006
Who are you quoting?
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OP really shouldn't show off. Especially when his grand revelations are just either basic facts or wrongheaded interpretations.
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>>8812130
who is this semen demon
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>>8812134
Chloe kiketz
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>>8812136
OP here where can I read more about the stuff on [math]L^p[/math] spaces on [math]L^p[/math] spaces?
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>>8812159
Depends on your field of interest (what you've described can bleed into functional analysis, CS, statistics, or even quantitative finance).
Off the top of my head you may want to look into spectral theory, and I'll namedrop Mercer's theorem because that's the main thing I remember from the stats class I took a long time ago.
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>>8812191
This seems very interesting to me. Do you have any literature or lecture notes you recommend?
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Saying "just vectors" is misleading because that's throwing away a ton of information and structure they have.
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>>8811006
>>integrals are just a way to sum uncountably many values that are zero
I like that one
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>>8811006
how the fuck could it take you so long?
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>>8811006
>realizing maths lets you say basic shit in a way that sounds advanced
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https://en.wikipedia.org/wiki/Function_space
Check this out
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>>8812405
>I like that one
It's wrong and even when you fix it, it is still really trivial.
It is wrong because you are not counting zeros, you are counting values really close to 0. So you fix it:
>Integrals are just a way to sum uncountably many values close to 0
But then you need to use 3 brain cells to remember that this is literally what the definition of the Riemann Integral is. So OP literally just came from a wikipedia article on integrals, misinterpreted it, and now thinks he has advanced in any way.
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>>8812558
You lack intuition.
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>>8812597
What intuition?
>Uhh hurrdurr look you are adding up rectangles with 0 area xD
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>>8812159
What would be the point of iterating the Lp space construction? Do you expect the resulting object to have some kind of universal property?
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Btw you need to specify a measure if you want to have an Lp space. In an infinite dimensional function space there is no canoncial Lebesgue measure.
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