AI 中文总结
研究局部紧李群\(\mathfrak{G}\)的模糊类似物\(\mathfrak{G_f}\)上模糊哈尔测度\(\mu_f\)的存在性，通过构造模糊哈尔积分，证明了在乘法常数意义下模糊哈尔积分的唯一性。
AI 中文摘要
设\(\mathfrak{G}\)为局部紧李群，\(d\mu\)为定义在\(\mathfrak{G}\)上的哈尔测度。我们考虑\(\mathfrak{G}\)的模糊类似物\(\mathfrak{G_f}\)（称为模糊李群）的存在性，并在\(\mathfrak{G_f}\)上建立模糊哈尔测度\(\mu_f\)。还构造了关于\(\mathfrak{G_f}\)上相应模糊哈尔测度的模糊哈尔积分，最后证明存在一个模糊哈尔积分，其在乘法常数意义下是唯一的。
英文摘要
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 $\mathfrak{G_f}$ called a fuzzy Lie group and develop a fuzzy Haar measure \(μ_f\) on $\mathfrak{G_f}$. Also we construct a fuzzy Haar integral with respect to the corresponding fuzzy Haar measure on $\mathfrak{G_f}$. And finally we show that there exists a fuzzy Haar integral that is unique up to a multiplicative constant.
CommentsarXiv admin note: text overlap with arXiv:0908.0254 by other authors
