## Thursday, March 14, 2013

### in which i feel like a fake .. (UPDATED)

sometimes i really question what i'm doing .. if i've really turned to the dark side of the force ..
1. on a set $X$, complement and union, strictly speaking, form .. well, a field on the collection $P(X)$ of all subsets of $X$. it happens that i'm in the setting where there is another set $X_1$ for which there is an .. er, field isomorphism from $P(X)$ onto $P(X_1)$ ..

.. and that's not all; this isomorphism gives rise to an isometric isomorphism from finitely-additive measures on $X$ to finite Borel regular measures on $X_1$.

ye gods: with words like field and isomorphism (and there's that hidden word functor around, somewhere) .. should i just hand in my resignation and rename this blog to the "frustrated pseudo-analyst" ..?

2. earlier today, i wrote that
"as usual, a measure here refers to a non-negative signed measure."

re-reading that sentence later, i felt slightly disgusted with myself .. and wondered how i came to this sorry state in my life.
// updated: 15 march 2013 @11:04EEST

the last few posts have been both strange and technical. i blame this on having been fully immersed in solving a recent problem .. to the point where i probably don't make much sense to people, including friends.

in fact, all this week it's taken quite the effort to switch from "maths mode" back to "human mode." i think i'm better now ..

.. well, depending on your definition of "better" ..! (-: