  Let $(S,\cdot)$ be a semigroup and $\mathfrak{m}$ be a $\sigma$-algebra on
$S$. We say $(S,\cdot,\mathfrak{m})$ is a measurable semigroup if $\pi:S\times
S\longrightarrow S$ by $\pi(x,y)=x\cdot y$ is a measurable function. In this
paper , we consider to $\mathfrak{m}^\beta$ as the collection of all
ultrafilters on $\mathfrak{m}$. We show that $\mathfrak{m}^\beta$ is a compact
right topological semigroup respect to generated topology by $\sigma$-algebra
$\mathfrak{m}$ on $\mathfrak{m}^\beta$. Also we study some elementary
properties of the algebraic structure of $\mathfrak{m}^\beta$.
