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 Jul 31 awarded Nice Question Dec 15 awarded Caucus Sep 24 awarded Autobiographer Sep 17 accepted Ask for a good reference for the calculus involving singular continuous measure Sep 17 awarded Commentator 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. Sep 16 asked Ask for a good reference for the calculus involving singular continuous measure Feb 27 accepted About the extreme value theorem over the extended real line 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 26 asked About the extreme value theorem over the extended real line Feb 24 accepted Looking for hints of this inequality 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.