Outer measureIn the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.
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.
EconomyAn economy is an area of the production, distribution and trade, as well as consumption of goods and services. In general, it is defined as a social domain that emphasize the practices, discourses, and material expressions associated with the production, use, and management of scarce resources. A given economy is a set of processes that involves its culture, values, education, technological evolution, history, social organization, political structure, legal systems, and natural resources as main factors.
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.
InstitutionInstitutions (singular: institution) are humanly devised structures of rules and norms that shape and constrain individual behavior. All definitions of institutions generally entail that there is a level of persistence and continuity. Laws, rules, social conventions and norms are all examples of institutions. Institutions vary in their level of formality and informality. Institutions are a principal object of study in social sciences such as political science, anthropology, economics, and sociology (the latter described by Émile Durkheim as the "science of institutions, their genesis and their functioning").
Multi-party systemIn political science, a multi-party system is a political system in which multiple political parties across the political spectrum run for national elections, and all have the capacity to gain control of government offices, separately or in coalition. Apart from one-party-dominant and two-party systems, multi-party systems tend to be more common in parliamentary systems than presidential systems and far more common in countries that use proportional representation compared to countries that use first-past-the-post elections.
Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Vector measureIn mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization of the concept of finite measure, which takes nonnegative real values only.
Economic historyEconomic history is the study of history using methodological tools from economics or with a special attention to economic phenomena. Research is conducted using a combination of historical methods, statistical methods and the application of economic theory to historical situations and institutions. The field can encompass a wide variety of topics, including equality, finance, technology, labour, and business. It emphasizes historicizing the economy itself, analyzing it as a dynamic entity and attempting to provide insights into the way it is structured and conceived.
Formative assessmentFormative assessment, formative evaluation, formative feedback, or assessment for learning, including diagnostic testing, is a range of formal and informal assessment procedures conducted by teachers during the learning process in order to modify teaching and learning activities to improve student attainment. The goal of a formative assessment is to monitor student learning to provide ongoing feedback that can help students identify their strengths and weaknesses and target areas that need work.
Political organisationA political organization is any organization that involves itself in the political process, including political parties, non-governmental organizations, and special interest advocacy groups. Political organizations are those engaged in political activities (e.g., lobbying, community organizing, campaign advertising, etc.) aimed at achieving clearly-defined political goals, which typically benefit the interests of their members.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
Summative assessmentSummative assessment, summative evaluation, or assessment of learning is the assessment of participants in an educational program. Summative assessments are designed to both assess the effectiveness of the program and the learning of the participants. This contrasts with formative assessment, which summarizes the participants' development at a particular time in order to inform instructors of student learning progress. The goal of summative assessment is to evaluate student learning at the end of an instructional unit by comparing it against a standard or benchmark.
Political partyA political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific ideological or policy goals. Political parties have become a major part of the politics of almost every country, as modern party organizations developed and spread around the world over the last few centuries. It is extremely rare for a country to have no political parties.
Political systemIn political science, a political system means the type of political organization that can be recognized, observed or otherwise declared by a state. It defines the process for making official government decisions. It usually comprizes the governmental legal and economic system, social and cultural system, and other state and government specific systems. However, this is a very simplified view of a much more complex system of categories involving the questions of who should have authority and what the government influence on its people and economy should be.
Politics of CanadaThe politics of Canada function within a framework of parliamentary democracy and a federal system of parliamentary government with strong democratic traditions. Canada is a constitutional monarchy, in which the monarch is head of state. In practice, the executive powers are directed by the Cabinet, a committee of ministers of the Crown responsible to the elected House of Commons of Canada and chosen and headed by the Prime Minister of Canada. Canada is described as a "full democracy", with a tradition of liberalism, and an egalitarian, moderate political ideology.
