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.
Sales operationsSales operations is a set of business activities and processes that help a sales organization run effectively, efficiently and in support of business strategies and objectives. Sales operations may also be referred to as sales, sales support, or business operations.
Sales managementSales management is a business discipline which is focused on the practical application of sales techniques and the management of a firm's sales operations. It is an important business function as net sales, through the sale of products and services and resulting profit, drive most commercial business. These are also typically the goals and performance indicators of sales management. Sales manager is the typical title of someone whose role is sales management. The role typically involves talent development.
Sales promotionSales promotion is one of the elements of the promotional mix. The primary elements in the promotional mix are advertising, personal selling, direct marketing and publicity/public relations. Sales promotion uses both media and non-media marketing communications for a pre-determined, limited time to increase consumer demand, stimulate market demand or improve product availability. Examples include contests, coupons, freebies, loss leaders, point of purchase displays, premiums, prizes, product samples, and rebates.
Sales (accounting)In bookkeeping, accounting, and financial accounting, net sales are operating revenues earned by a company for selling its products or rendering its services. Also referred to as revenue, they are reported directly on the income statement as Sales or Net sales. In financial ratios that use income statement sales values, "sales" refers to net sales, not gross sales. Sales are the unique transactions that occur in professional selling or during marketing initiatives. Revenue is earned when goods are delivered or services are rendered.
Integer programmingAn integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Optimizing compilerIn computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of optimizing transformations, algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster.
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.
Rough setIn computer science, a rough set, first described by Polish computer scientist Zdzisław I. Pawlak, is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the lower and the upper approximation of the original set. In the standard version of rough set theory (Pawlak 1991), the lower- and upper-approximation sets are crisp sets, but in other variations, the approximating sets may be fuzzy sets. The following section contains an overview of the basic framework of rough set theory, as originally proposed by Zdzisław I.
Null setIn mathematical analysis, a null set is a Lebesgue measurable set of real numbers that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length. The notion of null set should not be confused with the empty set as defined in set theory. Although the empty set has Lebesgue measure zero, there are also non-empty sets which are null. For example, any non-empty countable set of real numbers has Lebesgue measure zero and therefore is null.
