Bounded variation and Helly's selection theorem

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Bounded variation and Helly's selection theorem

Bounded variation vs. Helly's selection theorem

In mathematical analysis, a function of bounded variation, also known as function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. In mathematics, Helly's selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence.

Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.

Banach space and Bounded variation · Banach space and Helly's selection theorem · See more »

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

Bounded variation and Compact space · Compact space and Helly's selection theorem · See more »

Distribution (mathematics)

Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.

Bounded variation and Distribution (mathematics) · Distribution (mathematics) and Helly's selection theorem · See more »

Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

Bounded variation and Limit of a sequence · Helly's selection theorem and Limit of a sequence · See more »

Locally integrable function

In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition.

Bounded variation and Locally integrable function · Helly's selection theorem and Locally integrable function · See more »

Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

Bounded variation and Mathematical analysis · Helly's selection theorem and Mathematical analysis · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Bounded variation and Mathematics · Helly's selection theorem and Mathematics · See more »

Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

Bounded variation and Open set · Helly's selection theorem and Open set · See more »

Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

Bounded variation and Real line · Helly's selection theorem and Real line · See more »

Separable space

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

Bounded variation and Separable space · Helly's selection theorem and Separable space · See more »

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

Bounded variation and Sequence · Helly's selection theorem and Sequence · See more »

Total variation

In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.

Bounded variation and Total variation · Helly's selection theorem and Total variation · See more »