I am reading the book by B. Mordukhovich, Variational analysis and generalized differentiation I. On page 6 it is stated the following inclusion: $$ \hat{N}_{\varepsilon }\left( \bar{x};\Omega \right) \supset \hat{N}\left( \bar{x};\Omega \right) +\varepsilon \mathbb{B}^{\ast }. $$ $\mathbb{B}...

Could you please help to me to compute the following $\epsilon$-normal set: Given $\epsilon>0$, how to compute the $\epsilon$-normal set of $C:=[2,\infty)\times \Bbb{R}$ at the point $(2,0)$. Thank you in advanced! An $\epsilon$-normal set of a convex set $C \subset \Bbb{R}^n$ at a point $z \in C...

It is tagged as an open problem in the book Fractional parts,series and integrals. If this proof is valid , I don't have any idea how to get it published so I posted it here . $\displaystyle \sum_{a_1,a_2,\cdots,a_n=1}^\infty \frac{a_1a_2\cdots a_n}{(a_1+a_2+\cdots+a_n)!} = \; ?$ I am posting a...

I've come up with this question and I've been playing with it for a couple weeks by now without any definite breakthrough; it seems there should be a better approach than straight naive brute force, but I haven't come up with anything conclusive yet. (The work and partial answers I have come up ...