Jun Tanaka

collaborators

Showing math.FAShow all

2 papers · 1 filter

math.FA2008

An isomorphism between the completion of an Algebra and its Caratheodory Extension

Jun Tanaka

Let $Ω$ denote an algebra of sets and $μ$ a $σ$ -finite measure. We then prove that the completion of $Ω$ under the pseudometric $d (A, B)$ = $μ^{*} (A △ B)$ is $σ$ -algebra…

math.FA2007

A Realization of Measurable Sets as Limit Points

Jun Tanaka, Peter F. McLoughlin

Starting with a sigma finite measure on an algebra, we define a pseudometric and show how measurable sets from the Caratheodory Extension Theorem can be thought of as limit points…