counting measure

counting measure
A positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset.

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  • Counting measure — In mathematics, the counting measure is an intuitive way to put a measure on any set: the size of a subset is taken to be the number of elements in the subset, if the subset is finite, and ∞ if the subset is infinite.[1] Formally, start with a… …   Wikipedia

  • Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis …   Wikipedia

  • Counting of the Omer — Repentance in Judaism Teshuva Return Repentance, atonement and higher ascent in Judaism   …   Wikipedia

  • Counting (music) — In music, counting is a system of regularly occurring sounds that serve to assist with the performance or audition of music by allowing the easy identification of the beat. Commonly, this involves verbally counting the beats in each measure as… …   Wikipedia

  • measure — measurer, n. /mezh euhr/, n., v., measured, measuring. n. 1. a unit or standard of measurement: weights and measures. 2. a system of measurement: liquid measure. 3. an instrument, as a graduated rod or a container of standard capacity, for… …   Universalium

  • counting — The procedure of uniquely associating one number with each element of a set in order to arrive at a measure of the set. Along with measurement, counting is the procedure whereby mathematics is applied. Hence its objectivity is a principal datum… …   Philosophy dictionary

  • measure word — noun A word or morpheme used in combination with a numeral to indicate the count of nouns, used especially in Asian languages. Syn: count word, counter, counter word, counting word, numeral classifier …   Wiktionary

  • Locally finite measure — In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure.DefinitionLet ( X , T ) be a Hausdorff topological space and let Sigma; be a sigma; algebra on X that contains… …   Wikipedia

  • Information theory and measure theory — Measures in information theory = Many of the formulas in information theory have separate versions for continuous and discrete cases, i.e. integrals for the continuous case and sums for the discrete case. These versions can often be generalized… …   Wikipedia

  • Radon measure — In mathematics (specifically, measure theory), a Radon measure, named after Johann Radon, is a measure on the σ algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular. Contents 1 Motivation 2 Definitions …   Wikipedia

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