Lebesgue constant information

In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given...

the Riemann–Lebesgue lemma is a best possible result for continuous functions, and gives some treatment to Lebesgue constants. Lebesgue once wrote, "Réduites...

polynomials of degree n or less. The Lebesgue constant L is defined as the operator norm of X. One has (a special case of Lebesgue's lemma): ‖ f − X ( f ) ‖ ≤ (...

W. "Thue-Morse Constant". MathWorld. Weisstein, Eric W. "Golomb–Dickman Constant". MathWorld. Weisstein, Eric W. "Lebesgue Constants". MathWorld. Weisstein...

In measure theory, Lebesgue's dominated convergence theorem gives a mild sufficient condition under which limits and integrals of a sequence of functions...

like a constant one which cannot grow, and in another, it does indeed monotonically grow. It is also called the Cantor ternary function, the Lebesgue function...

after Henri Lebesgue: Blaschke–Lebesgue theorem Cantor–Lebesgue function Borel–Lebesgue theorem Fatou–Lebesgue theorem Lebesgue constant Lebesgue covering...

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

_{\infty })\inf _{p\in P_{n}}\lVert f-p\rVert } with the norm or Lebesgue constant of the Lagrange interpolation operator Ln of the nodes (t1, ..., tn + 1)...

condition than Lebesgue-integrability. The converse does not hold; not all Lebesgue-integrable functions are Riemann integrable. The Lebesgue–Vitali theorem...

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...

real analysis, measurable functions are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability...

early 20th century, Henri Lebesgue generalized Riemann's formulation by introducing what is now referred to as the Lebesgue integral; it is more general...

Lebesgue integral. A discrete random variable is sometimes defined as a random variable whose cumulative distribution function is piecewise constant....

Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali in 1905. The Vitali theorem is the...

the interpolation polynomial Bernstein polynomial Carlson's theorem Lebesgue constant The Chebfun system Table of Newtonian series Frobenius covariant Sylvester's...

theorem usually refers to a fundamental result in measure theory due to Lebesgue and Beppo Levi that says that for sequences of non-negative pointwise-increasing...

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

of given constant width. The Blaschke–Lebesgue theorem says that the Reuleaux triangle has the least area of any convex curve of given constant width. Every...

converges for all real ξ {\displaystyle \xi } , and (using the Riemann–Lebesgue lemma) that the transformed function f ^ {\displaystyle {\widehat {f}}}...

points in R2 with unique polynomial interpolant and minimal growth of Lebesgue constant Hermite interpolation Birkhoff interpolation Abel–Goncharov interpolation...

{\displaystyle L\cap (-m,m)} has Lebesgue measure zero. Consequently, so has L {\displaystyle L} . In contrast, the Lebesgue measure of the set of all real...

measurable subsets of Rd is a regular family (in the sense of Lebesgue) if there exists a constant C such that diam ⁡ ( V ) d ≤ C λ d ( V ) {\displaystyle \operatorname...