Construct · 2 fields · 4 citations

Where does measure collide?

One name. Different field. Different construct. One map.

● jingle · one word, two constructs Nearest construct by meaningmeasurementcompare the meanings
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Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to measure is measurement.

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measure2 CONSTRUCTSMeasure (math)BOREL · SIZE OF A SETMeasure (scale)CAMPBELL · ATTRIBUTE SCALE

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1898Measure (math)1920Measure (scale)
2026

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Mathematics

a set function assigning a non-negative size such as length, area, or probability, additive over disjoint countable parts.

Borel introduced in 1898 (Lecons sur la theorie des fonctions) a way to assign a non-negative size to subsets of the number line, so that the size of a whole equals the sum of the sizes of its disjoint countable parts. Lebesgue's 1902 Integrale, longueur, aire extended this into a general theory in which a measure is a set function giving length, area, volume, or probability, and it underlies modern integration. Here a measure is a rule that attaches a number to a set of points, and it has nothing to do with a grouping of musical beats or the numbering of an attribute in a survey.[1][2]

Unit
A set function assigning a non-negative number (length, area, volume, or probability) to a set
Recovery means
Not applicable
Measured by
Defined axiomatically by non-negativity, zero on the empty set, and countable additivity over a sigma-algebra of measurable sets

Measurement and psychometrics

Numbers assigned to an attribute

Campbell's 1920 Physics: The Elements set out measurement as the assignment of numbers to represent the magnitude of an attribute of an object, separating quantities that can be added from those that cannot. Stevens's 1946 On the theory of scales of measurement generalized this to the nominal, ordinal, interval, and ratio scales, and in this tradition a measure is the instrument or operation that turns an attribute into a number. This referent is a mapping from objects to numbers standing for how much of a property they have, unlike a size attached to a set of points or a group of beats in a bar of music.[3][4]

Unit
One measurement: a number placed on a nominal, ordinal, interval, or ratio scale to stand for an attribute
Recovery means
Not applicable
Measured by
Judged by the scale type attained and by the reliability and validity of the operation that assigns the numbers

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Nearby collisions

integral3 fields · 4 citationsjingle · one word, three constructsscale3 fields · 3 citationsjingle · one word, three constructsmeter2 fields · 2 citationsjingle · one word, two constructsmeasurement3 fields · 5 citationsjingle · one word, three constructs

References

  1. Borel, E. (1898). Lecons sur la theorie des fonctions. Gauthier-Villars.
  2. Lebesgue, H. (1902). Integrale, longueur, aire. Annali di Matematica Pura ed Applicata, 7(1), 231-359. https://doi.org/10.1007/BF02420592
  3. Campbell, N. R. (1920). Physics: The elements. Cambridge University Press.
  4. Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677-680. https://doi.org/10.1126/science.103.2684.677

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