For a metric space $(X,d)$ and a dimension function $\varphi:[0,\infty)\to[0,\infty)$ we can define a metric outer measure $H_\varphi$ which is $\varphi$-Hausdorff measure. Since it is a metric outer ...
Let $RP^n$ be the $n$-dim real projective space. I have the following four questions. What is the so called standard metric on $RP^n$? More generally, consider a metric space $M$ with an equivalent ...
Reference:- Evans-Gariepy, Federer, other books and notes of geometric measure thoery. I just want to clarify whether these definitions of measure theoretic interior and boundary are correct. Given ...
Let $(X,d)$ be a metric space and $\mu$ a probability measure. Let $f(x)=\mu(B(x,r))$. Is this map upper semi continuous? I have some other assumptions since this is part of a larger proof but I'm ...
Where can I find the Theorem of invariance of the dimension with diffeomorphisms? And about Between Homeomorphism? I also want to know about the Hausdorff dimension invariance what is deeper!
The following various definitions of a Radon measure seem to be given for the Borel sigma algebra of different types of topological spaces: general, Hausdorff, locally compact, or locally compact ...