# precisely+bounded

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**Central Asia, history of**— Introduction history of the area from prehistoric and ancient times to the present. In its historical application the term Central Asia designates an area that is considerably larger than the heartland of the Asian continent. Were it… …62

**Bolzano–Weierstrass theorem**— In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite dimensional Euclidean space R^n. The theorem states that each bounded sequence in R^n has a convergent subsequence. An equivalent formulation… …63

**Dirac delta function**— Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …64

**Path integral formulation**— This article is about a formulation of quantum mechanics. For integrals along a path, also known as line or contour integrals, see line integral. The path integral formulation of quantum mechanics is a description of quantum theory which… …65

**Total variation**— As the green ball travels on the graph of the given function, the length of the path travelled by that ball s projection on the y axis, shown as a red ball, is the total variation of the function. In mathematics, the total variation identifies… …66

**Hardy-Littlewood maximal function**— In mathematics, the Hardy Littlewood maximal operator M is a significant non linear operator used in real analysis and harmonic analysis. It takes a function f (a complex valued and locally integrable function) : f:mathbb{R}^{d} ightarrow… …67

**Singular integral**— In mathematics, singular integrals are central to abstract harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular intetgral is an integral operator: T(f)(x) = int K(x,y)f(y) ,… …68

**Capacity of a set**— In mathematics, the capacity of a set in Euclidean space is a measure of that set s size . Unlike, say, Lebesgue measure, which measures a set s volume or physical extent, capacity is a mathematical analogue of a set s ability to hold electrical… …69

**Burnside's problem**— The Burnside problem, posed by William Burnside in 1902 and one of the oldest and most influential questions in group theory, asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. In… …70

**Marcinkiewicz interpolation theorem**— In mathematics, the Marcinkiewicz interpolation theorem, discovered by Józef Marcinkiewicz (1939), is a result bounding the norms of non linear operators acting on Lp spaces. Marcinkiewicz theorem is similar to the Riesz–Thorin theorem about …