#measure-theory — Public Fediverse posts

Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich

This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.

Revised English Edition
Translated and Edited by Richard A. Silverman

You can get the book here and here.

#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral

I was told to share this motivational meme I made today.

#measuretheory #maths

`Kakutani's theorem is a fundamental result on the equivalence or mutual singularity of countable product measures. It gives an "if and only if" characterisation of when two such measures are equivalent, and hence it is extremely useful when trying to establish change-of-measure formulae for measures on function spaces.`

https://en.wikipedia.org/wiki/Kakutani's_theorem_(measure_theory)

#measureTheory #math #mathematics #integrability

New almostsure blog post: Non-measurable sets

#measuretheory

https://almostsuremath.com/2023/07/16/non-measurable-sets/

youtube.com/@xenaproject
for #mathematics #mathsbasics#mathematicallogic #sets #logic #topology #numbertheory #linearalgebra
#probability #measuretheory
#functionalanalysis

A third (!) amazing thing I’ve learned today!

(This one’s a bit less accessible than the other two, as it requires some mathematical knowledge)

There is, it seems, a strictly monotone polynomial-valued measure for subsets of R^n

Video: https://youtube.com/watch?v=h_CFMtRQiek

Preprint: https://arxiv.org/abs/2008.09969

#mathematics #MeasureTheory #topology

I love how #measuretheory simplifies the understanding to introduction of #statistics

I'm looking for work! My current funding runs out soon, so I'm looking for what's next. More contract work? Full-time employment? Something else?

Most of my work has been in #julialang, developing #foss packages for probabilistic programming (#probprog) and #measuretheory. More generally, I'm interested in #bayesian #stats, performance algorithms, composability, and #functionalprogramming. I love learning and #mentoring, and I've been a team lead and IC, enjoying both.

Please retoot!