All Questions

Let $ B $ be the set of all measures $ \phi $ of $ \mathbf{R}^{n} $ such that every open set is $ \phi $-measurable (sometimes these measures are called Borel measures). Note the measures in $ B $ are ...

Is there a notion of dimension such that for all Borel sets $A,B\subseteq\mathbb{R}^{n}$ we have $$ \dim(A\times B)=\dim(A)+\dim(B)?$$ For topological, Minkowski, packing and Hausdorff dimension this ...

$\mathcal{N}_u$ : Class of all uncountable Lebesgue-null set i.e all uncountable sets having Lebesgue outer measure $0$. Let $f:\Bbb{R}\to \Bbb{R}$ be a function with the following property : $\...

Let $V$ be a normed space and $(V_j)_{j\in [0,1]}$ be a family of linear subspaces of $V$ with $V_1$ non-trivial and such that $V_1\subsetneq V_j\subseteq V_i$ whenever $i\leq j$. We write $W:=V'$ for ...