Nebenmaß

Nebenmaß, also known as a "side measure" or "auxiliary measure," is a concept in measure theory. It refers to a measure that is related to another, typically more fundamental or primary, measure on the same measurable space. Often, a Nebenmaß is derived from the main measure through some form of transformation or operation. For example, it might be a restriction of the main measure to a subset, or a modification of the main measure by a density function. The term is not as universally standardized as "measure" itself, and its specific definition can depend on the context of the mathematical work. In some instances, a Nebenmaß might be used to analyze properties of the primary measure or to construct new measures with specific characteristics. The relationship between the Nebenmaß and the original measure is crucial for understanding its properties and applications.