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A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the σ-algebra) and the method that is used for measuring (the measure). One important example of a measure space is a probability space.
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While MS-DOS and NT always treat the suffix after the last period in a file's name as its extension, in UNIX-like systems, the final period does not necessarily mean that the text after the last period is the file's extension. [1] Some file formats, such as .txt or .text, may be listed multiple times.
Given a (possibly incomplete) measure space (X, Σ, μ), there is an extension (X, Σ 0, μ 0) of this measure space that is complete. [3] The smallest such extension (i.e. the smallest σ-algebra Σ 0) is called the completion of the measure space. The completion can be constructed as follows:
File size is a measure of how much data a computer file contains or how much storage space it is allocated. Typically, file size is expressed in units based on byte. A large value is often expressed with a metric prefix (as in megabyte and gigabyte) or a binary prefix (as in mebibyte and gibibyte). [1]