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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://math.stackexchange.com/q/3518516
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https://math.stackexchange.com/questions/242877/compact-support-functions-dense-in-l-1
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https://mathproblems123.files.wordpress.com/2011/02/density-1.pdf
Oct 03, 2004 · 1 Approximation by continuous functions 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.
https://mathoverflow.net/questions/237636/are-compactly-supported-continuous-functions-dense-in-the-continuous-functions-o
Continuous functions on $\mathbb R^d$ such that the support is a compact subset of $\overline{\Omega}$? For "nice" $\Omega$ this would be the space of continuous functions on $\Omega$ vanishing at the boundary. $\endgroup$ – Jochen Wengenroth Apr 29 '16 at 12:50
https://mathoverflow.net/questions/267710/continuous-functions-dense-in-l-1
$\begingroup$ @AryehKontorovich In an infinite dimensional Banach space, an open ball is not precompact, and the support of a nonzero continuous function contains some open ball, so it is not compact.
http://www.math.ucsd.edu/~bdriver/231-02-03/Lecture_Notes/Chapter%2011-%20Convolutions%20and%20Approximations.pdf
continuous functions with compact support) is dense in L p (µ) for all p∈[1,∞).
https://en.wikipedia.org/wiki/Support_(mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero. If the domain of f is a topological space, the support of f is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis
https://www.chegg.com/homework-help/questions-and-answers/2-prove-space-cc-r-continuous-functions-compact-support-dense-lp-r-1-q43198402
2. Prove that the space Cc(R") of all continuous functions with compact support is dense in LP(R™) for 1<p < 0.
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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