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https://math.stackexchange.com/questions/242877/compact-support-functions-dense-in-l-1
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https://www.encyclopediaofmath.org/index.php/Function_of_compact_support
The support of is the closure of the set of points for which is different from zero . Thus one can also say that a function of compact support in is a function defined on such that its support is a closed bounded set located at a distance from the boundary of by a number greater than , where is sufficiently small.
https://www.planetmath.org/CompactlySupportedContinuousFunctionsAreDenseInLp
We denote by C c (X) the space of continuous functions X → ℂ with compact support. Theroem - For every 1 ≤ p < ∞, C c (X) is dense in L p (X) (http://planetmath.org/LpSpace).
https://en.wikipedia.org/wiki/Support_(mathematics)
In good cases, functions with compact support are dense in the space of functions that vanish at infinity, but this property requires some technical work to justify in a given example.
http://www.math.nthu.edu.tw/~kchen/teaching/5131week3.pdf
dense in Lp(E). These step functions are linear combinations of characteristic functions on some dyadic cubes. This implies that the space of simple functions is also dense in Lp(Rn). In this section we prove that the space of smooth functions with compact supports, and the space of functions with rapidly decreasing derivatives are also dense in L(Rn).
http://www.math.ucsd.edu/~bdriver/231-02-03/Lecture_Notes/Chapter%2011-%20Convolutions%20and%20Approximations.pdf
such that µ(K) <∞when Kis a compact subset of X.Then Cc(X) (the space of continuous functions with compact support) is dense in L p (µ) for all p∈[1,∞). Proof.
https://mathproblems123.files.wordpress.com/2011/02/density-1.pdf
Oct 03, 2004 · In this supplement, we’ll show that continuous functions with compact support are dense in L1 = L1(Rn;m). The support of a complex valued function f on a metric space X is the closure of fx 2 X : f(x) 6= 0g. We’ll denote by Cc(X) the set of all complex valued continuous functions on X with compact support. It should be noted
https://en.wikipedia.org/wiki/Compact_star
It would grow to include exotic stars if such hypothetical, dense bodies are confirmed to exist. All compact objects have a high mass relative to their radius, giving them a very high density, compared to ordinary atomic matter.
https://www.curseforge.com/minecraft/mc-mods/compact-ores
Compact Ores. CompactOres is a Minecraft mod that adds ores which yield extra resources. This mod is heavily inspired by RWTema's Dense Ores.. Features. A compact ore is a block which mimics an ore from Minecraft or another mod.
http://www.math.ucsd.edu/~bdriver/240A-C-03-04/Lecture_Notes/Older-Versions/chap22.pdf
of continuous functions with compact support) is dense in L p (µ) for all p∈ [1,∞).(See also Proposition 25.23 below.)
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