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Associated with Math.SE; for both general discussion & math qu...
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learning_mathematician
May 6, 2020 11:22
some help please: If f,g∈L1, can someone give me a case where the convolution f*g is not continuous at 0.
learning_mathematician
May 6, 2020 11:16
does anyone have experience with measure theory
learning_mathematician
May 6, 2020 11:14
@StupidKid here is the link
tinyurl.com/cfqcvpc
learning_mathematician
May 6, 2020 11:13
some help please: If f,g$\in{L^1}$, can someone give me a case where the convolution f*g is not continuous at 0.
learning_mathematician
May 5, 2020 21:00
@Thorgott in some instances you have continuity sets, which are the points where a function f is continuous
learning_mathematician
May 5, 2020 20:58
@Thorgott I don't think sets are continuous, but functions between sets may be
learning_mathematician
May 5, 2020 20:55
@Thorgott it means that the pre-image of an open set is open
learning_mathematician
May 5, 2020 20:25
yes the $E_n$ are pairwise disjoint
learning_mathematician
May 5, 2020 20:24
in need help with something real quick: $χ_{⋃E_n}$=∑$χ_{E_n}$ note χ is the inidicator function
learning_mathematician
May 5, 2020 20:22
hi everyone
learning_mathematician
May 5, 2020 11:25
so $\chi_{\cup E_n}$
learning_mathematician
May 5, 2020 11:16
for the second part for the indicator function of the union of $E_n$ that is $X_{⋃En}$=∑χEn.
should I just show what the indicator/characteristic function of the union of $E_n$ looks like?
learning_mathematician
May 5, 2020 11:15
it works
learning_mathematician
May 5, 2020 11:14
let's try $\mu$
learning_mathematician
May 5, 2020 11:12
thanks robjohn
learning_mathematician
May 5, 2020 11:12
done
learning_mathematician
May 5, 2020 10:58
@robjohn yes
learning_mathematician
May 5, 2020 10:50
@robjohn bookmarklet?
learning_mathematician
May 5, 2020 10:46
should I just show what the indicator/characteristic function of the union of En looks like?
learning_mathematician
May 5, 2020 10:46
for the second part for the indicator function of the union of En that is X_(⋃En)=∑χEn.
learning_mathematician
May 5, 2020 10:41
I see so μf(∅)=∫∅ f which clearly is 0 since the integral of f over nothing is 0
learning_mathematician
May 5, 2020 10:36
I know this is a basice question but I don't like having doubts
learning_mathematician
May 5, 2020 10:36
or should I take the μf(EU∅)=μf(E)+μf(∅)
learning_mathematician
May 5, 2020 10:35
should I just let E=0 so that ∫fχ∅=∫f0=0?
learning_mathematician
May 5, 2020 10:33
so to show μf(emptyset)=0
learning_mathematician
May 5, 2020 10:30
so to show μf is a measure on E, I must prove the criteria, μf(empty set)=0, pairwise disjointness of En's and union=sum
learning_mathematician
May 5, 2020 10:27
In a measure space (X,μ), let f ∈L1 and f≥0. for every measurable set E let μf=∫Ef = ∫XfχE
1) show μf is a measure do I have to show that f induces a measure on E of X?
learning_mathematician
May 5, 2020 10:26
@AlessandroCodenotti haha ok
learning_mathematician
May 5, 2020 10:23
does any of you have some measure theory experience?
learning_mathematician
May 5, 2020 10:23
hello everyone
