The Usual Metric

#Mathematics #Calculus #Realanalysis #Measuretheory #Foundations

https://sciencehumor.io/math-memes/the-usual-metric-wfhl

Just released: Proof of the Riemann Hypothesis via Haar inversion + functional equation + Peter-Weyl compactness.

Preprint:
doi.org/10.5281/zeno...

Feedback welcome!

#RiemannHypothesis #NumberTheory #Math #MeasureTheory #Primes #ComplexAnalysis #MathSky #NumberSky #ZetaZeros

I've started a little side project to port the MeasureTheory semantics to Rust. Hard to say whether it will go anywhere, currently it's a lot of exploring the design space and learning more about good ways to set up traits

Toupin, D. (2025). Holding the Line: How Haar Measure, Functional Symmetry, and Compactness Force the Riemann Hypothesis. Zenodo. doi.org/10.5281/zeno...

#Skyence #NumberTheory #SpectralTheory #MeasureTheory #ComplexAnalysis #BrownianMotion #RiemannHypothesis #ZetaFuction #MillenniumPrizeProblems

Consider this a footnote to this morning's meme.
#mathematics #math #SetTheory #MeasureTheory
Source:https://buff.ly/My0nnIz

#mathematics #math #MeasureTheory #AxiomofChoice #humor

3/5
Von Neumann algebras are generated by their projections, meaning any element can be approximated by linear combinations of projections. This is analogous to how simple
#functions
are dense in L∞ spaces in classical #measuretheory.

Fun Fact: While Blaise #Pascal and Pierre de #Fermat are some of the first mathematicians to formalize #probability by thinking about games of chance, it was Andrey #Kolmogorov who was responsible for axiomatizing probability using the, then, new field of math, #measuretheory.

Yoshikata Kida shows that for certain HNN extensions, including Baumslag–Solitar groups, the kernel of the modular homomorphism is measure equivalent to an infinite-rank free group × ℤ: doi.org/10.1142/S179...

#GroupTheory #MeasureTheory #Algebra

My first thought was to build something like MeasureTheory but based mainly on exponential families. This does ok, but we can do better.