We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.

中文翻译：

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热带埃哈特理论和热带体积

我们在热带几何学中引入了一个新颖的内在体积概念。这是通过开发多表位中点数计数的热带模拟的基础来实现的。我们展示基本属性并将其与现有度量进行比较。通过对出现的复杂性问题的简要研究来补充我们的论述。