measure theory - ορισμός. Τι είναι το measure theory
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Τι (ποιος) είναι measure theory - ορισμός

FUNCTION ASSIGNING NUMBERS TO SOME SUBSETS OF A SET, WHICH COULD BE SEEN AS A GENERALIZATION OF LENGTH, AREA, VOLUME AND INTEGRAL
Measure theory; Measure (measure theory); Mathematical measure; Measurable set; Positive measure; Measurable; Countably additive measure; Countably additive function; Countable additivity property; Measure Theory; Measure theoretic
  • Countable additivity of a measure <math>\mu</math>: The measure of a countable disjoint union is the same as the sum of all measures of each subset.
  • monotone]] in the sense that if <math>A</math> is a [[subset]] of <math>B,</math> the measure of <math>A</math> is less than or equal to the measure of <math>B.</math> Furthermore, the measure of the [[empty set]] is required to be 0. A simple example is a volume (how big an object occupies a space) as a measure.

Measurable         
·adj Moderate; temperate; not excessive.
II. Measurable ·adj Capable of being measured; susceptible of mensuration or computation.
measurable         
a.
1.
Mensurable.
2.
Moderate, temperate.
measurable         
¦ adjective able or large enough to be measured.
Derivatives
measurability noun
measurably adverb

Βικιπαίδεια

Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general.

The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Constantin Carathéodory, and Maurice Fréchet, among others.