We're doing sigma algebras in my math class, and my first reaction to the term is ugh, what coping Internet bro thing is it this time? Like an algebra that *could* have loads of sex, honest, but is such a chad that it doesn't need it anyway
February 3, 2026 at 6:12 AM
We're doing sigma algebras in my math class, and my first reaction to the term is ugh, what coping Internet bro thing is it this time? Like an algebra that *could* have loads of sex, honest, but is such a chad that it doesn't need it anyway
sí, si es más que me lo he visto y me ha disgustado. tampoco tiene pinta de ser muy complicado, si es sigma álgebra que hay que probar la unión finita todavía pero esto no debería ser mucho. a lo mejor algo del complementario es complicado a lo sumo
January 6, 2026 at 8:50 PM
sí, si es más que me lo he visto y me ha disgustado. tampoco tiene pinta de ser muy complicado, si es sigma álgebra que hay que probar la unión finita todavía pero esto no debería ser mucho. a lo mejor algo del complementario es complicado a lo sumo
Yes and no - my applied math mind treats the entire training space of a model as a giant sigma-algebra. It's just that humans haven't traversed that but I can see how the average ready would misread that.
Such is inherently the beauty of generative models!
Such is inherently the beauty of generative models!
December 16, 2025 at 8:15 PM
Yes and no - my applied math mind treats the entire training space of a model as a giant sigma-algebra. It's just that humans haven't traversed that but I can see how the average ready would misread that.
Such is inherently the beauty of generative models!
Such is inherently the beauty of generative models!
sir i have a sigma algebra right here and it assigns the empty set measure 0 and the whole sample space measure 1
November 18, 2025 at 4:15 AM
sir i have a sigma algebra right here and it assigns the empty set measure 0 and the whole sample space measure 1
I think the hard part there is pinning down how the interventions and outcomes are selected. I don't even think you can come up with a well-posed probability distribution over "interventions." What's the sigma-algebra?
November 15, 2025 at 5:26 PM
I think the hard part there is pinning down how the interventions and outcomes are selected. I don't even think you can come up with a well-posed probability distribution over "interventions." What's the sigma-algebra?
Okay this is embarrasing but I as a semi-mature probabilist only recently realized that the event {S_n = 0 infinitely often} is not in the tail sigma algebra (where S_n denotes a simple random walk, idk S_n = X_1 + ... + X_n for X_i iid centred e.g.). It is still in the exchangeable algebra though!
November 11, 2025 at 6:54 PM
Okay this is embarrasing but I as a semi-mature probabilist only recently realized that the event {S_n = 0 infinitely often} is not in the tail sigma algebra (where S_n denotes a simple random walk, idk S_n = X_1 + ... + X_n for X_i iid centred e.g.). It is still in the exchangeable algebra though!
Oh so it’s just the idea of taking a classical random variable X on a triple (event space, sigma algebra, a probability function) which maps to R, restricting to a smaller sigma algebra but being able to extend that back out
November 6, 2025 at 8:38 PM
Oh so it’s just the idea of taking a classical random variable X on a triple (event space, sigma algebra, a probability function) which maps to R, restricting to a smaller sigma algebra but being able to extend that back out
Okay no I walked in there on purpose. Borel sigma algebra
October 10, 2025 at 3:54 AM
Okay no I walked in there on purpose. Borel sigma algebra
getting fired for starting intro stat by defining a sigma algebra
Statistics without calculus is also an atrocity
Physics without calculus is an atrocity.
October 2, 2025 at 6:04 PM
getting fired for starting intro stat by defining a sigma algebra
In ogni testo dove la probabilità la fa da padrona (per applicazioni pratiche), i primi due capitoli spiegano correttamente gli spazi campionari come un’esempio di una sigma-algebra (o algebra di Borel). Ogni volta mi tocca rinfrescarmi la memoria… Pensare che imparai la P con urne e palline 🏳️ e 🏴
September 30, 2025 at 8:09 PM
In ogni testo dove la probabilità la fa da padrona (per applicazioni pratiche), i primi due capitoli spiegano correttamente gli spazi campionari come un’esempio di una sigma-algebra (o algebra di Borel). Ogni volta mi tocca rinfrescarmi la memoria… Pensare che imparai la P con urne e palline 🏳️ e 🏴
Jetzt ist deine Sigma-Algebra in der bedingten Erwartung leider schon zu groß
September 21, 2025 at 3:04 PM
Jetzt ist deine Sigma-Algebra in der bedingten Erwartung leider schon zu groß
1/Technically, a probability measure is a sigma-algebra that has results in the unit interval [0,1] and is countably additive. In other words, you can decrease by more than 100%. The problem is, you then decrease by an amount that's less than 1 cent. EG: $1000*.00001 = .001.
September 19, 2025 at 4:50 AM
1/Technically, a probability measure is a sigma-algebra that has results in the unit interval [0,1] and is countably additive. In other words, you can decrease by more than 100%. The problem is, you then decrease by an amount that's less than 1 cent. EG: $1000*.00001 = .001.
Tetsuya Hattori: Choquet integration with submodular function on measurable space with sigma-algebra generating chain https://arxiv.org/abs/2509.11033 https://arxiv.org/pdf/2509.11033 https://arxiv.org/html/2509.11033
September 16, 2025 at 6:40 AM
Tetsuya Hattori: Choquet integration with submodular function on measurable space with sigma-algebra generating chain https://arxiv.org/abs/2509.11033 https://arxiv.org/pdf/2509.11033 https://arxiv.org/html/2509.11033
the only one of these that I actually haven't seen in the wild is (3) but still. seems like there's no obvious path
![What's the "dual" of a set $A$ with some operations $A^n \to A$ for some $n$?
1. **Comodels**: Of course, the dual of $A \times A$ must be $A + A$, so an $X$-ary function $A^X \to A$ has dual $$A \to X \cdot A$$ where $X \cdot A$ is just the $X$-fold coproduct $A + \dots + A$.
2. **Co-operations**: Of course, the dual of $A^2 = [2, A]$ must be $[A, 2] = 2^A$, so an $X$-ary function $A^X \to A$ has dual $$1^A \to X^A$$ which is, equivalently, an element of $X^A = [A, X]$.
3. **Co-structure of a signature:** For each $n < \omega$, let $F_n$ be the set of function symbols of arity $n$ in the signature $\Sigma$. Then a $\Sigma$-structure is a function $F_n \times A^n \to A$ for each $n < \omega$. Dually, a co-structure of $\Sigma$ should be a function $$A \to F_n \times A^n$$ for each $n < \omega$.
4. **Polynomial coalgebra**: A function $A \times A \to A$ is an algebra of the polynomial endofunctor $p: A \mapsto A^2$, so the answer should be a coalgebra of $p$, that is, a set $A$ and a function $A \to A \times A$. In general, we consider coalgebras of polynomial endofunctors, i.e. a set $A$ and a function $$A \to \sum_n X_n \cdot A^n$$](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:judtbidg6b2ye3jzverecw3g/bafkreidqsbqjxm5sxhl4byhcohbv3znavdihwqwz44uolhle6jguzazcom@jpeg)
September 12, 2025 at 10:18 PM
the only one of these that I actually haven't seen in the wild is (3) but still. seems like there's no obvious path
Counting sheep but first I need some measure space sigma algebra thing.
September 6, 2025 at 3:42 PM
Counting sheep but first I need some measure space sigma algebra thing.
sigma-algebra implies the existence of sigma algebraists (this is awful im so sorry you are all allowed to kill me for this😭😭)
August 16, 2025 at 11:50 PM
sigma-algebra implies the existence of sigma algebraists (this is awful im so sorry you are all allowed to kill me for this😭😭)
It's useful to prove results about convergence.
But it's also useful to represent available info accumulating over time. The collection of events that are known to happen or not is a sigma-algebra and a measurable function is one whose value we can work out from that information.
But it's also useful to represent available info accumulating over time. The collection of events that are known to happen or not is a sigma-algebra and a measurable function is one whose value we can work out from that information.
August 15, 2025 at 11:37 PM
It's useful to prove results about convergence.
But it's also useful to represent available info accumulating over time. The collection of events that are known to happen or not is a sigma-algebra and a measurable function is one whose value we can work out from that information.
But it's also useful to represent available info accumulating over time. The collection of events that are known to happen or not is a sigma-algebra and a measurable function is one whose value we can work out from that information.
The “fanaticism” option is to augment your current sigma-algebra with a singular Doom event. That’s not really a workable model of a large world, it’s a model of our ignorance about it.
August 11, 2025 at 10:05 PM
The “fanaticism” option is to augment your current sigma-algebra with a singular Doom event. That’s not really a workable model of a large world, it’s a model of our ignorance about it.
I think just coarse sigma-algebras can do it. In your example, B can be too fine, but some other C containing B can also be in the sigma-algebra.
August 10, 2025 at 2:55 PM
I think just coarse sigma-algebras can do it. In your example, B can be too fine, but some other C containing B can also be in the sigma-algebra.
In that literature, your state of knowledge is captured by your sigma-algebra since that describes all the states of the world you can distinguish. Probability is just a numerical assessment of that, and is largely incidental.
August 10, 2025 at 2:08 PM
In that literature, your state of knowledge is captured by your sigma-algebra since that describes all the states of the world you can distinguish. Probability is just a numerical assessment of that, and is largely incidental.
Okay ngl I'm not exactly sure what is another definition of E[X]? Should we go via the moment-generating function? Should we use the Lebesgue-Integral over the sigma algebra? Does that really make such a massive difference? To me the integral over g(x) always was the definition of it
August 7, 2025 at 9:00 PM
Okay ngl I'm not exactly sure what is another definition of E[X]? Should we go via the moment-generating function? Should we use the Lebesgue-Integral over the sigma algebra? Does that really make such a massive difference? To me the integral over g(x) always was the definition of it
My students: "Logistic Regression predicts probabilities, not continuous values"
Ah, yes, the classic case of probabilities. It's either gonna happen (1) or not (0). No in between. Go home, Sigma-Algebra, we don't need you here.
Ah, yes, the classic case of probabilities. It's either gonna happen (1) or not (0). No in between. Go home, Sigma-Algebra, we don't need you here.
Me during teaching: "People will tell you that Logistic Regression is not a regression technique but that's not true, it predicts continuous probabilities"
Me in the exam: "Is Logistic Regression a regression technique?"
My students: "No it's classification"
Me in the exam: "Is Logistic Regression a regression technique?"
My students: "No it's classification"
July 19, 2025 at 8:26 AM
My students: "Logistic Regression predicts probabilities, not continuous values"
Ah, yes, the classic case of probabilities. It's either gonna happen (1) or not (0). No in between. Go home, Sigma-Algebra, we don't need you here.
Ah, yes, the classic case of probabilities. It's either gonna happen (1) or not (0). No in between. Go home, Sigma-Algebra, we don't need you here.
Decryption:
In the beginning was the sample space (all potential outcomes - raw, undivided possibility).
And the sigma-algebra said: "Let there be subsets" (measurable slivers of reality, sliced from the infinite).
Structure was born. And with it - selection, exclusion, fate.
In the beginning was the sample space (all potential outcomes - raw, undivided possibility).
And the sigma-algebra said: "Let there be subsets" (measurable slivers of reality, sliced from the infinite).
Structure was born. And with it - selection, exclusion, fate.
July 19, 2025 at 12:52 AM
Decryption:
In the beginning was the sample space (all potential outcomes - raw, undivided possibility).
And the sigma-algebra said: "Let there be subsets" (measurable slivers of reality, sliced from the infinite).
Structure was born. And with it - selection, exclusion, fate.
In the beginning was the sample space (all potential outcomes - raw, undivided possibility).
And the sigma-algebra said: "Let there be subsets" (measurable slivers of reality, sliced from the infinite).
Structure was born. And with it - selection, exclusion, fate.
In the beginning was the sample space. And the sigma-algebra said:
"Let there be subsets."
And the void complied, closing itself under union and dread.
"Let there be subsets."
And the void complied, closing itself under union and dread.
July 19, 2025 at 12:52 AM
In the beginning was the sample space. And the sigma-algebra said:
"Let there be subsets."
And the void complied, closing itself under union and dread.
"Let there be subsets."
And the void complied, closing itself under union and dread.
my p doom? sorry that's not a valid sigma algebra
June 23, 2025 at 11:45 PM
my p doom? sorry that's not a valid sigma algebra