Lebesgue space information

Lebesgue space may refer to: Lp space, a special Banach space of functions (or rather, equivalence classes of functions) Standard probability space, a...

to integrate on spaces more general than the real line. The Lebesgue integral provides the necessary abstractions for this. The Lebesgue integral plays...

finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according...

probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous) is a probability space satisfying...

measure Lebesgue's number lemma Lebesgue point Lebesgue space Lebesgue spine Lebesgue's universal covering problem Lebesgue–Rokhlin probability space Lebesgue–Stieltjes...

-norm. It is therefore important to develop a tool for differentiating Lebesgue space functions. The integration by parts formula yields that for every u...

Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in...

measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure...

The Lebesgue spaces appear in many natural settings. The spaces L2(R) and L2([0,1]) of square-integrable functions with respect to the Lebesgue measure...

It follows, for example, that the Lebesgue space L p ( [ 0 , 1 ] ) {\displaystyle L^{p}([0,1])} is a Hilbert space only when p = 2. {\displaystyle p=2...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional...

infinite-dimensional vector spaces. An important development of vector spaces is due to the construction of function spaces by Henri Lebesgue. This was later formalized...

Lebesgue's dominated convergence theorem. Let ( f n ) {\displaystyle (f_{n})} be a sequence of complex-valued measurable functions on a measure space...

In 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...

are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable. Let...

equilateral dimension has been particularly studied for Lebesgue spaces, finite-dimensional normed vector spaces with the L p {\displaystyle L^{p}} norm   ‖ x ‖...

Lebesgue differentiation theorem Lebesgue integration Lebesgue measure Infinite-dimensional Lebesgue measure Lebesgue point Lebesgue space Lebesgue–Rokhlin...

problem of product spaces. Suppose that we have already constructed Lebesgue measure on the real line: denote this measure space by ( R , B , λ ) . {\displaystyle...

In mathematics, the Lebesgue differentiation theorem is a theorem of real analysis, which states that for almost every point, the value of an integrable...

|f(x)|^{p}\;dx\right)^{1/p}} is a seminorm on the vector space of all functions on which the Lebesgue integral on the right hand side is defined and finite...

justify than in Lebesgue integration. It is easy to extend the Riemann integral to functions with values in the Euclidean vector space R n {\displaystyle...

the dimension as vector space is finite if and only if its Krull dimension is 0. For any normal topological space X, the Lebesgue covering dimension of...

\mathbb {R} } is separable. The Lebesgue spaces L p ( X , μ ) {\displaystyle L^{p}\left(X,\mu \right)} , over a measure space ⟨ X , M , μ ⟩ {\displaystyle...