Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
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 magnitude, 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.
Complete measureIn mathematics, a complete measure (or, more precisely, a complete measure space) is a measure space in which every subset of every null set is measurable (having measure zero). More formally, a measure space (X, Σ, μ) is complete if and only if The need to consider questions of completeness can be illustrated by considering the problem of product spaces. Suppose that we have already constructed Lebesgue measure on the real line: denote this measure space by We now wish to construct some two-dimensional Lebesgue measure on the plane as a product measure.
Synaptic plasticityIn neuroscience, synaptic plasticity is the ability of synapses to strengthen or weaken over time, in response to increases or decreases in their activity. Since memories are postulated to be represented by vastly interconnected neural circuits in the brain, synaptic plasticity is one of the important neurochemical foundations of learning and memory (see Hebbian theory). Plastic change often results from the alteration of the number of neurotransmitter receptors located on a synapse.
Commodity status of animalsThe commodity status of animals is the legal status as property of most non-human animals, particularly farmed animals, working animals and animals in sport, and their use as objects of trade. In the United States, free-roaming animals (ferae naturae) are (broadly) held in trust by the state; only if captured can be claimed as personal property. Animals regarded as commodities may be bought, sold, given away, bequeathed, killed, and used as commodity producers: producers of meat, eggs, milk, fur, wool, skin and offspring, among other things.
Animal testingAnimal testing, also known as animal experimentation, animal research, and in vivo testing, is the use of non-human animals in experiments that seek to control the variables that affect the behavior or biological system under study. This approach can be contrasted with field studies in which animals are observed in their natural environments or habitats. Experimental research with animals is usually conducted in universities, medical schools, pharmaceutical companies, defense establishments, and commercial facilities that provide animal-testing services to the industry.
NeurofeedbackNeurofeedback is a type of biofeedback that focuses on the neuronal activity of the brain. The training method is based on reward learning (operant conditioning) where a real-time feedback provided to the trainee is supposed to reinforce desired brain activity or inhibit unfavorable activity patterns. Different mental states (for example, concentration, relaxation, creativity, distractibility, rumination, etc.) are associated with different brain activities or brain states.
ParadigmIn science and philosophy, a paradigm (ˈpærədaɪm ) is a distinct set of concepts or thought patterns, including theories, research methods, postulates, and standards for what constitute legitimate contributions to a field. The word paradigm is Greek in origin, meaning "pattern", and is used to illustrate similar occurrences. Paradeigma Paradigm comes from Greek παράδειγμα (paradeigma), "pattern, example, sample" from the verb παραδείκνυμι (paradeiknumi), "exhibit, represent, expose" and that from παρά (para), "beside, beyond" and δείκνυμι (deiknumi), "to show, to point out".
Borel measureIn mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require additional restrictions on the measure, as described below. Let be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of ; this is known as the σ-algebra of Borel sets. A Borel measure is any measure defined on the σ-algebra of Borel sets.
Animal rightsAnimal rights is the philosophy according to which many or all sentient animals have moral worth independent of their utility to humans, and that their most basic interests—such as avoiding suffering—should be afforded the same consideration as similar interests of human beings. Broadly speaking, and particularly in popular discourse, the term "animal rights" is often used synonymously with "animal protection" or "animal liberation".
