All Questions

I want to prove that the function $F: \mathbb{R}_+ \to \mathbb{R}$ defined by $$F(t)=\int_{\{d=t\}} g \, d\mathcal{H}^{n-1}$$ is continuous if $g:\Omega \subset \mathbb{R}^n\to \mathbb{R}$ is ...

Lebesgue's differentiation theorem states that if $x$ is a point in $\mathbb{R}^n$ and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lebesgue integrable function, then the limit of $\frac{\int_B f d\...

Let $X$ be a smooth manifold, and denote by $\Omega^*(X)$ the set of all smooth differential forms on $X$. Assume we have a family of differential forms $\omega_t \in \Omega^*(X)$, $t\in E$, ...

Looking at the generalizations of Stokes theorem, I did find a version for manifold with corners, but I was surprised this generalization doesn't contain a simple example such as the cone. So my ...

If $M$ is a smooth manifold and $\mu$ is a $1$-density thereon then we may define a Borel measure (on Borel sets $A$) on $M$ as: \begin{equation} \nu(A) = \int_M I_A \mu. \end{equation} My question ...

I have recently come across the book The Kurzweil-Henstock Integral and its Differentials by Solomon Leader, in which, if I understand correctly, the HK integration process is modified in a way that ...