Does anybody here know a relatively self-contained resource where I can read up about fubini-tonelli for bochner integrals (on separable spaces)

ya mum's chest hair

it needs a scientist-physicist-mathematician-philosopher much like einstein to piece together, to grasp, to formulate, to announce.

Not necessarily for general banach spaces, for Hilbert spaces suffices and should be considerably simpler. Showing the equality between exchanged integrals should be relatively easy using functionals, but measurability of integrating out one coordinate could be meh. Or obvious, who knows

youre close! o_O

There's a theorem that strong measurability is equivalent to concatenations with functionals being measurable (I think). maybe I have to go through that and then it's easy

@EdwardEvans sorry ard

weeeyyyy

one thing i will admit frustration with

i know lots of relatively self-contained resources where you can not read about that

frustration?

@Thorgott can you link them all?

thanks

when people talk about the problems with pilot wave theory: if they bring up relativity theory, then I will nod in agreement with the problems raised

but if we're talking about non-relativistic QM? pilot wave seems entirely fine there

i'm not frustrated by people bringing up relativistic objections. but non-relativistic objections genuinely seem to miss the point when i see them

look plz look into that collapse experiment cited. youre very good on the historical stuff, but history is being made right now, already... the Big Questions are increasingly experimentally testable/ tested, some have already been tested and the implications arent being fully understood yet.

let me put it another way.

how about some further serious/ in depth discussion of this excellent tour de force... even... peer review :) arxiv.org/abs/1910.10688

@Thorgott Thinking more about your example, it works for the $\alpha$ given in the book because $1 + x^3 + 1 \equiv x^3 $ in $k$ of characteristic 2, so $x^2$ does divide $x^3$

the $\alpha$ would be $\frac{\sqrt{1} - \sqrt{x^3 + 1}}{x}$

↑ lol rare praise/ excitement o_O

that's in the context of linear programming / polyhedra, to be clear

and indeed that stuff is Neat.

haha dude why do you disappear? whats the problem here? the "context" is more than LP/ polyhedra ofc

uh

no

i was there for that conversation

Balarka was talking about linear programming, and how that relates to the geometry of polyhedra

we were not talking about QM

← can also read conversations... YOU were talking about QM etc

to the extent that polyhedra connect to Bell's inequality, it's on the local realism side

for QM you get smooth convex bodies like the elliptope

yes, havent heard Balarka say much about QM. was searching that for some amusement once...

am aware of the analogy, just cited it!

whereof I cannot speak thereof I remain silent

Such a devout Wittgensteinean

Wittgenstein would probably tell me to shut the fuck up tbh

LOL! "speak of the devil!"™

lol

what did wittgenstein say about this? alas yes, not in on all the inside jokes, of which there are many with Balarka :( ... Balarka plz choose some nickname you deserve it :)

speechless huh? some more inside jokes in the meantime

Henrik could be a good nickname

Because Henrik I B Sen

ha

HenRick and Morty

lol its a start, think need something more "poetic/ evocative"

all we are saying is, give QC/ QM a chance! genius.com/Plastic-ono-band-give-peace-a-chance-lyrics

can weak measurability of function with values in separable banach spaces be reduced to weak measurability with respect to a countable number of linear functionals?

Nobody cares, tosser

goddammit

@#%& sigh lol

@user2103480 i'd be surprised if false

@Semiclassical nice chatting maybe gotta run the energy seems to have disappeared for the moment, anyway am sure theres some more great papers on the subj looking fwd to next one, hope you overcome the silence to talk about it in detail sometime/ someday :) chat.stackexchange.com/rooms/9446/theory-salon

Me too. At least for the only sensible option, the borel-sigma algebra, this seems to be true. Specifically, for any separable Banach space $U$, there is a countable set of linear functionals such that the sigma algebra generated by that set is the Borel $\sigma$-algebra on $U$.

So that one can test measurability exactly by concatenating with functionals. Also, this directly proves the pettis theorem on measurability I think

I probably implicitly assumed that the sigma-algebra on the banach space is the borel algebra anyways

Ok nice then I have a proof of Fubini for Bochner integrals, I think

Oi its snowing outside, haven't seen that in a while

@user2103480 What do you think of Burial

Great artist, but most songs miss the feels-center just by an inch

I dont have a clue why though, and it is exclusively due to my personal taste. Idk why, but listening in the dark to his most famous album doesn't induce what it should induce

I think I like Near Dark and In McDonalds the most. And you?

(removed)

(removed)

$\Huge{\left(\mathfrak{removed}\right)}$

Nothing to see here.

@EdwardEvans You're gonna get flagged

flag away bois

boisson

@EdwardEvans lol

Flagges auxais boisson

I swear every time I look at Alexander Gruber's message, instead of DEAR MATH ROOM I read DEATH ROOM and have to look again

Is it just me?

Nah I could get with that

My favourite bit is "you're making Math.SE look bad"

implying it isn't actually bad

No no, it's not the guys that make yo mama jokes that's the problem, it's those flag 'em

can we officially re-brand to DEATH ROOM

that would be very metal, I think

Death.Stack

with the caps, of course

I think that would greatly diminish the traffic

Or at least change the population

for the better or for the worse?

Who am I to judge?

@vzn Thanks for thinking of me! Unfortunately my back burner got suddenly busy during the week so my light reading time evaporated!

@user586228 that's a lot of questions. Did you figure out what the probs. were for passing exactly 0,1,2,3 exams was (call these $p_0,...,p)3$, they clearly sum to one)? The question asked to compute $pcm$ which, if independent, corresponds to the probability of passing all three exams which is $p_3$.