Computable measure theory information

In mathematics, computable measure theory is the part of computable analysis that deals with effective versions of measure theory. Jeremy Avigad (2012)...

Church–Turing thesis, which states that any function that is computable by an algorithm is a computable function. Although initially skeptical, by 1946 Gödel...

recursive numbers, effective numbers or the computable reals or recursive reals. The concept of a computable real number was introduced by Emile Borel in...

cube System F Introduction to topos theory LF (logical framework) Computability logic Computable measure theory Finitism Ultraintuitionism Luitzen Egbertus...

Information Theory, IRE Transactions on. 2 (3). IEEE: 113–124. doi:10.1109/TIT.1956.1056813. S2CID 19519474. Alan Turing (1937). "On computable numbers,...

to solve the problem. The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all...

measures are used in many parts of analysis, number theory, group theory, representation theory, statistics, probability theory, and ergodic theory....

preferred over other theories-of-everything by Occam's Razor. Tegmark also considers augmenting the MUH with a second assumption, the computable universe hypothesis...

2^{*}} be a computable function mapping finite binary strings to binary strings. It is a universal function if, and only if, for any computable f : 2 ∗ →...

theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably...

the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what...

complexity theory the Blum axioms or Blum complexity axioms are axioms that specify desirable properties of complexity measures on the set of computable functions...

Netherlands Stevens, S.S. On the theory of scales and measurement 1946. Science. 103, 677–80. Douglas Hubbard: "How to Measure Anything", Wiley (2007), p....

PMID 19797653. S2CID 17187000. Manin, Yu. I. (1980). Vychislimoe i nevychislimoe [Computable and Noncomputable] (in Russian). Soviet Radio. pp. 13–15. Archived from...

Lebesgue measure. In the mathematical theory of probability, we confine our study to a probability measure μ, which satisfies μ(E) = 1. Lebesgue's theory defines...

In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables...

science, neurobiology, physics, and electrical engineering. A key measure in information theory is entropy. Entropy quantifies the amount of uncertainty involved...

to optimize some measure of performance such as minimizing the number of mistakes made on new samples. Computational number theory, also known as algorithmic...

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the...

definition of a computable simple game. In particular, all finite games are computable. Kumabe, M.; Mihara, H. R. (2011). "Computability of simple games:...

not a probability and it is not computable. It is only "lower semi-computable" and a "semi-measure". By "semi-measure", it means that 0 ≤ ∑ x P ( x )...

and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied...

J. F. Knight, 2000. Computable Structures and the Hyperarithmetical Hierarchy, Elsevier. ISBN 0-444-50072-3 Computability Theory of Hyperarithmetical...

other computable p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} . Here, "Church" refers to Alonzo Church, whose 1940 paper proposed using Turing-computable rules...