Outer Measure
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Outer Measure
In the mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ... field of measure theory Measure is a fundamental concept of . Measures provide a mathematical abstraction for common notions like , /, , , of events, and — after — . These seemingly distinct concepts are innately very similar and may, in many cases, be treated a ..., an outer measure or exterior measure is a function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ... defined on all subsets of a given set with values in the extended real numbers In mathematics, the affinely extended real number system is ...
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Mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus about its exact scope or . Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of . These objects are either s from nature (such as s or "a "), or (in modern mathematics) abstract entities that are defined by their basic properties, called s. A consists of a succession of applications of some to already known results, including previously proved s, axioms and (in case of abstraction from nature) some basic properties that are considered as true starting points of the theory under consideration. The result of a proof is called a ''theorem''. Contrary to s, the validity of a theorem (its truth) does not rely on any but on the correctness of its reasoning (though experimentation is often useful for ...
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