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seen Sep 28 at 17:31

I am a math student. Thanks for many warm-hearted professors, students here to offer their helps. :-)


Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
I see, Thanks Yemon Choi.
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
I agree. According to the Lebesgue's decomposition theorem, $\mu$ has three parts. I study them separately. The absolutely continuous part is easy; the pure jump part reduces to the study of the Dirac delta measure. The problem arises if the singular continuous part is not vanishing, I need to prove something. Thanks a lot!
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
@Nate Eldredge, okay, thanks. :)
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
thanks a lot! I agree. But all information that I know about my measure $\mu$ is that it is a singular continuous (nonnegative) measure. In this setting, do you have any idea to construct a sequence of measures $\mu_n$ that converge to $\mu$ in the weak sense? Is there a general construction procedure? Thank you very much!
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
Thanks Nate Eldredge for your help! Do you have a reference for this so that I can learn it more systematically? In my problem, I have a general singular continuous measure, not necessary the Cantor measure. Thanks a lot!
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
Nate Eldredge, may I know what is Math.SE? Thanks.
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
Thanks Nate Eldredge! :)
Sep
17
comment Ask for a good reference for the calculus involving singular continuous measure
Yemon Choi, people working on stochastic calculus might have this knowledge as well.
Feb
26
comment About the extreme value theorem over the extended real line
Thanks Brian M. Scott. :-)
Feb
26
comment About the extreme value theorem over the extended real line
Thanks WimC. :-)
Feb
24
comment Looking for hints of this inequality
Dear Professor Julián Aguirre, Thank you very much for your solutions. Even we restrict x,y,z to be real numbers, by letting x=1 and y=-z=R, the second inequality will fail as R tends to infinite. Thanks a lot.
Feb
24
comment Looking for hints of this inequality
In my research, I would like to have this inequality. These inequalities are my guess. For sure, I can modify accordingly. It is related to the Poisson kernel and fractional heat equations.
Jan
29
comment A paradox on Hilbert spaces and their duals
Thank Professors Byron Schmuland and Matthew Daws for your nice answer and nice comment. I am clear now. :-)