UNIVERSALLY MEASURABLE Meaning and
Definition
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Universally measurable is a term used in mathematics, particularly in measure theory, to describe a set that possesses a certain property of measurability. In the context of probability and measure theory, a set is said to be universally measurable if it can be assigned a measure in a consistent and meaningful way, allowing for the notion of probability to be defined for that set.
More specifically, a set is universally measurable if it is measurable with respect to any measure on the underlying space. This means that the set can be divided into subsets that can be assigned a measure, allowing for the calculation of probabilities for events occurring within that set.
Universally measurable sets possess the property of being well-behaved with respect to measures, as they can be consistently and reliably measured regardless of the specific measure used. Such sets are a fundamental concept in understanding and modeling probabilistic events and phenomena.
In summary, a set is considered universally measurable when it can be assigned a measure in a consistent and meaningful way, allowing for the calculation of probabilities within that set. These sets are regarded as well-behaved and are an essential component of measure theory and probability theory.
Etymology of UNIVERSALLY MEASURABLE
The word "universally measurable" is composed of two main parts: "universal" and "measurable".
The term "measurable" comes from the verb "measure", which can be traced back to the Latin "mensurare", meaning "to measure". In English, "to measure" refers to determining the dimensions, quantity, amount, or degree of something using a standard unit or system. The suffix "-able" denotes the capability or possibility of performing an action or possessing a quality.
The term "universal" comes from the Latin word "universus", meaning "whole" or "entire". In English, "universal" refers to something that applies to all or is true for everyone, without exception. The suffix "-al" in "universal" is used to form adjectives.
Therefore, when putting both parts together, "universally measurable" describes something that is capable of being measured and applicable without exception.
