Haar Measure on Fuzzy Lie Group

Abstract

Let $\mathfrak{G}$ be a locally compact Lie group and \(dμ\) a Haar measure defined on $\mathfrak{G}$. We consider the existence of a fuzzy analogue of $\mathfrak{G}$ denoted by ${\mathfrak{G}}_{\mathfrak{f}}$ called a fuzzy Lie group and develop a fuzzy Haar measure \(μ_f\) on ${\mathfrak{G}}_{\mathfrak{f}}$. Also we construct a fuzzy Haar integral with respect to the corresponding fuzzy Haar measure on ${\mathfrak{G}}_{\mathfrak{f}}$. And finally we show that there exists a fuzzy Haar integral that is unique up to a multiplicative constant.

arXiv admin note: text overlap with arXiv:0908.0254 by other authors