论文标题
通过限制卷积力对适当凹锥的限制确定的措施
Measures Determined by the Restriction of Convolution Powers to the Proper Concave Cone
论文作者
论文摘要
令$μ$和$ν$为两个在适当的凸锥上定义的两个非排斥有限签名的Borel措施。我们证明，如果$μ$和$ν$的所有卷积功率在适当的凹锥上适当地等于（和非零），则量度相等。可以在[2]中找到类似但更一般的结果。我们还提供了二维措施的示例，这表明措施平等及其在半平面上的适当卷积能力不足以使措施平等。
Let $μ$ and $ν$ be two non-degenerate finite signed Borel measures defined on a proper convex cone of $\mathbb{R}^n$. We prove that if all convolution powers of $μ$ and $ν$ are appropriately equal (and non-zero) on a proper concave cone of $\mathbb{R}^n$, the measures are equal. A similar but more general result for measures defined on $\mathbb{R}$ can be found in [2]. We also provide an example of two-dimensional measures, which indicates that equality of measures and their appropriate convolution powers on a half-plane is not enough for equality of measures.
