Jun Tanaka

collaborators

4 papers

math.GM2008

Modern Set

Jun Tanaka

In this paper, we intend to generalize the classical set theory as much as possible. we will do this by freeing sets from the regular properties of classical sets; e.g., the law of…

math.LO2008

Fuzzy signed measure

Jun Tanaka

we will define a fuzzy signed measure on $σ$ -algebras, as well as positive and negative sets. Herein, we will show that the Fuzzy Hahn Decomposition Theorem, which is a generalizat…

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…