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Aug
25
answered As of August 2015, is the “set” of all gold medalists in the 2016 Olympics a set?
Aug
15
answered Is “random variable” really random?
Aug
12
comment counter examples for Riemann and Lebesgue integrabilities
@MoseWintner I got this book but found no such examples there.
Aug
8
comment counter examples for Riemann and Lebesgue integrabilities
@RamiroGuerreiro I agree with the theorem you mentioned. In fact it was that theorem motivated my question: I want to know what happens in other cases.
Aug
8
comment counter examples for Riemann and Lebesgue integrabilities
@zhw. When I said Riemann integral I actually included the improper case (implicitly by saying the interval may be unbounded). Sorry for my unclear statement.
Aug
8
revised counter examples for Riemann and Lebesgue integrabilities
added 692 characters in body; edited title
Aug
8
revised counter examples for Riemann and Lebesgue integrabilities
added 308 characters in body
Aug
8
revised counter examples for Riemann and Lebesgue integrabilities
added 308 characters in body
Aug
8
comment counter examples for Riemann and Lebesgue integrabilities
@Nitin Riemann integrability does NOT imply Lebesgue integrability in general: e.g. "alternating series" $(-1)^n\frac{1}{n}1 _{(n,n+1)}$and $\frac{\sin x}{x}$
Aug
8
comment counter examples for Riemann and Lebesgue integrabilities
@zhw. Why? $1/x^2$ is Riemann integrable over $[1,\infty)$
Aug
8
asked counter examples for Riemann and Lebesgue integrabilities
Aug
8
awarded  Critic
Aug
8
comment Showing $\frac{\sin x}{x}$ is NOT Lebesgue Integrable on $\mathbb{R}_{\ge 0}$
"$|f|$ is not Riemann integrable" does not imply that "$f$ is not Lebesgue integrable".
Jul
2
accepted $\|\sum_ia_i g(x-i)\|_{L^p(\mathbb{R})}\le (\sup_x \{\sum_k|g(x-k)|\})\|a\|_{L^p(\mathbb{Z})}$
Jun
20
answered $\|\sum_ia_i g(x-i)\|_{L^p(\mathbb{R})}\le (\sup_x \{\sum_k|g(x-k)|\})\|a\|_{L^p(\mathbb{Z})}$
Jun
20
asked $\|\sum_ia_i g(x-i)\|_{L^p(\mathbb{R})}\le (\sup_x \{\sum_k|g(x-k)|\})\|a\|_{L^p(\mathbb{Z})}$
May
15
asked number of distinct numbers of the form $e(k^2(4a)^{-1})$
May
9
comment an inequality on convolution
BTW, do you think it is possible to use $(1+|x-y|)^{-1}\le (1+|y|)(1+|x|)^{-1}$ to give a proof for $-N$ decay?
May
8
comment an inequality on convolution
Thank you. In fact what I really meant in my question was $-N$, not $N$
May
8
accepted an inequality on convolution