exterior measure

简明释义

外测度

英英释义

例句

1.When surveying land, it's important to take the exterior measure to ensure accurate property boundaries.

在测量土地时，重要的是进行外部测量以确保财产边界的准确性。

2.In construction, understanding the exterior measure is crucial for proper material estimation.

在建筑中，了解外部测量对正确的材料估算至关重要。

3.The real estate agent provided the exterior measure of the property to potential buyers.

房地产经纪人向潜在买家提供了该物业的外部测量。

4.The architect calculated the exterior measure of the building to determine the amount of siding needed.

建筑师计算了建筑物的外部测量以确定所需的外墙材料数量。

5.The exterior measure of the garden was taken to plan for fencing and landscaping.

为了规划围栏和景观设计，测量了花园的外部测量。

作文

The concept of exterior measure is fundamental in the field of mathematics, particularly in measure theory. It refers to a method of assigning a size or volume to a set in a way that can be applied to more complex shapes and regions. This approach allows mathematicians to extend the notion of length, area, and volume beyond simple geometric figures to more complicated sets that may not be easily defined by traditional means. Understanding the exterior measure involves recognizing its application in various mathematical contexts, such as integration and probability.To grasp the significance of exterior measure, one must first appreciate the limitations of conventional measures. For instance, the length of a line segment is straightforward to calculate, but when dealing with irregular shapes, such as fractals or sets with intricate boundaries, traditional methods fall short. The exterior measure provides a solution by using a covering approach, where the set in question is covered by a collection of open sets, and the total measure of these covering sets is computed. This process allows for a more flexible and comprehensive understanding of size.In practical terms, the exterior measure can be utilized in various fields, including physics, engineering, and computer science. For example, in physics, understanding the exterior measure of a region can help in calculating properties like mass or charge distribution over irregularly shaped objects. In computer science, algorithms that involve spatial analysis often rely on concepts derived from measure theory, where exterior measure plays a crucial role in determining the efficiency of data processing.Moreover, the exterior measure is essential in the development of Lebesgue measure, which is a cornerstone of modern analysis. The transition from exterior measure to Lebesgue measure illustrates the evolution of mathematical thought, showcasing how abstract concepts can lead to profound implications in real-world applications. By establishing a rigorous framework for measuring complex sets, mathematicians have opened new avenues for research and exploration.In conclusion, the exterior measure is not merely a theoretical construct; it is a powerful tool that enhances our understanding of mathematical concepts and their applications. As we continue to explore the intricacies of mathematics, the importance of exterior measure will only grow, highlighting the need for a solid foundation in measure theory for anyone aspiring to delve deeper into the subject. Through its application across various disciplines, the exterior measure proves to be an indispensable element in the broader landscape of mathematics, bridging the gap between abstract theory and practical application.

“外部测度”这一概念在数学领域，尤其是测度理论中，是基础性的。它指的是一种为集合分配大小或体积的方法，这种方法可以应用于更复杂的形状和区域。这种方法使得数学家能够将长度、面积和体积的概念扩展到不容易用传统方式定义的更复杂的集合。理解“外部测度”涉及到认识其在各种数学背景下的应用，例如积分和概率。要理解“外部测度”的重要性，首先必须欣赏传统测量的局限性。例如，线段的长度很容易计算，但在处理不规则形状时，例如分形或具有复杂边界的集合，传统方法就显得力不从心。“外部测度”通过覆盖方法提供了解决方案，其中所讨论的集合被一系列开集覆盖，并计算这些覆盖集的总测度。这个过程允许对大小有更灵活和全面的理解。在实际应用中，“外部测度”可以在物理学、工程学和计算机科学等多个领域中得到利用。例如，在物理学中，理解一个区域的“外部测度”可以帮助计算不规则形状物体的质量或电荷分布。在计算机科学中，涉及空间分析的算法通常依赖于测度理论衍生的概念，其中“外部测度”在确定数据处理效率方面发挥着关键作用。此外，“外部测度”在勒贝格测度的发展中至关重要，而勒贝格测度是现代分析的基石。从“外部测度”到勒贝格测度的转变展示了数学思想的演变，突显了抽象概念如何导致现实世界应用中的深远影响。通过建立测量复杂集合的严谨框架，数学家们为研究和探索开辟了新的途径。总之，“外部测度”不仅仅是一个理论构造；它是一个增强我们对数学概念及其应用理解的强大工具。随着我们继续探索数学的复杂性，“外部测度”的重要性只会增加，强调了任何希望深入研究该主题的人都需要扎实的测度理论基础。通过在各个学科中的应用，“外部测度”证明了自己在数学广阔领域中不可或缺的元素，架起了抽象理论与实际应用之间的桥梁。