论文标题
通用签名措施的连续定理，并应用于Karamata的Tauberian定理
A continuity theorem for generalised signed measures with an application to Karamata's Tauberian theorem
论文作者
论文摘要
$ \ mathbb {r} _ {+} $在且仅当其分布函数在限制度量的连续性时收敛时，拉普拉斯在$ \ mathbb {r} _ {+} $上转换了阳性度量。我们将这种经典的连续性定理扩展到广义签名的ra措施的情况。签名情况的结果需要一些其他条件，这是根据签名ra的模糊收敛性的最新结果。作为一种应用，我们引入了一种新型的Tauberian条件，用于扩展Karamata的Tauberian定理的广义符号ra。
The Laplace transforms of positive measures on $\mathbb{R}_{+}$ converge if and only if their distribution functions converge at continuity points of the limiting measure. We extend this classical continuity theorem to the case of generalised signed Radon measures. The result for the signed case requires some additional conditions, which follow from recent results on vague convergence of signed Radon measures. As an application, we introduce a novel Tauberian condition for generalised signed Radon measures that extends Karamata's Tauberian theorem.
