Maßsatz

Maßsatz is a German term that translates to "measure sentence" or "measurement rule" and is most commonly encountered in the context of mathematical and physical theorems, particularly in measure theory. It refers to a statement or proposition that establishes a fundamental property or relationship concerning measures, which are functions that assign a non-negative value (representing size or volume) to subsets of a given set. These theorems often dictate how measures behave under certain operations, such as union, intersection, or transformations, or they may define the conditions under which a measure exists or is unique. Examples include the Radon-Nikodym theorem, which relates different measures, or theorems about the continuity or integrability of functions with respect to a given measure. The "Maßsatz" provides the theoretical framework for quantifying and analyzing sets and their properties in a rigorous mathematical setting, forming a cornerstone for probability theory, functional analysis, and various branches of applied mathematics and physics.