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I am a PhD student at University of Alberta.


16h
revised norm of integral operator in $C([0,1])$
added 12 characters in body
23h
comment there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
Is it possible for $|\nu|(A) = 0$ with $\nu(A)\neq 0$?
1d
revised norm of integral operator in $C([0,1])$
deleted 15 characters in body
1d
answered norm of integral operator in $C([0,1])$
1d
comment there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
OK. The revised version should work. :)
1d
revised there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
fixed broken argument
1d
comment there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
You thanked me too soon. This argument may not work. I'll think about this more and post back. My apologies.
1d
comment there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
no problem! I made one more edit, sorry!
1d
comment there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
Sorry for the edits, my initial answer introduced issues that weren't necessary and also errantly assumed that $f$ is continuous!
1d
answered there is a measurable function $f$ on $X$ such that $|{f(x)}|=1$ for a.a $x \in X$ and $\nu(E)=\int_Efd|{\nu}|$ for any $E \in \mathfrak{M}$
1d
comment Are these proofs valid? Which method of proof is better?
Althought jnh's proof is elegant. Depending on your level of study, I feel it is an excellent habit to start with considering one direction at a time. And then afterwards simplifying your argument.
1d
comment Are these proofs valid? Which method of proof is better?
Your proof is fine, as long as the fact you stated is already established. By the way, writing your arguments out in full detail like this is a great way to set yourself up for success in mathematics. :)
2d
comment Axiomatizing topology through continuous maps
Sorry for my deleted answer. I realized afterwards I was drastically oversimplifying your question.
2d
comment Show that $f(\bar A) \implies \overline{f(A)}$.
The line $f(\overline{A})\Rightarrow \overline{f(A)}$ does not make mathematical sense. Are you trying to show that, for a continuous map $f$ of metric spaces, that $f(\overline{A})\subset \overline{f(A)}$? Nobody can confirm if your solution is correct or not until you tell us what exactly the problem is that you are solving!
2d
revised Complexification the real inner product space
added more detail
2d
revised Eigenvalues and eigenvectors of Linear Operator?
deleted 32 characters in body
2d
comment Does memorizing a proof help to provide the intuition behind it?
OK to make the question more concrete, lets work under the assumption that you follow the proof fully from assumption to conclusion, you find the proof completely acceptable, but aren't clueing into the idea behind it.
2d
asked Does memorizing a proof help to provide the intuition behind it?
2d
accepted Jordan Decomposition in a Vector Lattice
2d
comment Complexification the real inner product space
Please edit your question to include the details of what you have tried, so I can better help you.