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Short-term memory has limited capacity and is often referred to as "working-memory", however these are not the same. Working memory involves a different part of the brain and allows you to manipulate it after initial storage. The information that travels from sensory memory to short-term memory must pass through the Attention gateway. The ...
A Lebesgue measurable function is a measurable function : (,) (,), where is the -algebra of Lebesgue measurable sets, and is the Borel algebra on the complex numbers. Lebesgue measurable functions are of interest in mathematical analysis because they can be integrated.
The left adjoint: of the adjunction above is the identity on objects, and on morphisms it gives the canonical Markov kernel induced by a measurable function described above. As mentioned above, one can construct a category of probability spaces and measure-preserving Markov kernels as the slice category ( H o m S t o c h ( 1 , − ) , S t o c h ...
Memory is a complex system that relies on interactions between many distinct parts of the brain. In order to fully understand memory, researchers must cumulate evidence from human, animal, and developmental research in order to make broad theories about how memory works. Intraspecies comparisons are key.
Let (,,) be a measure space, i.e. : [,] is a set function such that () = and is countably-additive. All functions considered in the sequel will be functions :, where = or .We adopt the following definitions according to Bogachev's terminology.
The vector space of (equivalence classes of) measurable functions on (,,) is denoted (,,) (Kalton, Peck & Roberts 1984). By definition, it contains all the , and is equipped with the topology of convergence in measure.
The classical definition of a locally integrable function involves only measure theoretic and topological [4] concepts and can be carried over abstract to complex-valued functions on a topological measure space (X, Σ, μ): [5] however, since the most common application of such functions is to distribution theory on Euclidean spaces, [2] all ...
In general, any measurable function can be pushed forward. The push-forward then becomes a linear operator, known as the transfer operator or Frobenius–Perron operator.In finite spaces this operator typically satisfies the requirements of the Frobenius–Perron theorem, and the maximal eigenvalue of the operator corresponds to the invariant measure.