New almostsure blog post: Non-measurable sets

#measuretheory

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

https://www.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

Here is a #math question from a line of my #economics research:

There are functions which are discontinuous everywhere (Dirichlet function) and non-monotonic continuous but non-differentiable everywhere functions (Weierstrass function). Can a monotonic function be continuous but non-differentiable everywhere? Can the Lebesgue integral of a non-negative discontinuous everywhere function yield a continuous but non-differentiable everywhere function?

#MathMonday #realanalysis #measuretheory

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