monotonic functions and sequences S. N. Bernstein (1928). "Sur les fonctions absolument monotones". Acta Mathematica. 52: 1–66. doi:10.1007/BF02592679. D. Widder...

introduced by Hausdorff in 1921. The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics...

the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily jump...

convergence des séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données". Journal für die reine und angewandte...

Moreover, the fact that the set of non-differentiability points for a monotone function is measure-zero implies that the rapid oscillations of Weierstrass'...

and when it is possible to take limits under the integral sign (via the monotone convergence theorem and dominated convergence theorem). While the Riemann...

atomic class"?". Kadets 2018, p. 45. Sierpinski, W. (1922). "Sur les fonctions d'ensemble additives et continues" (PDF). Fundamenta Mathematicae (in...

obtain various theorems on invariant sets, e.g. the Ok's theorem: For the monotone map F : P(X ) → P(X ) on the family of (closed) nonempty subsets of X,...

was established by Peter Gustav Lejeune Dirichlet in 1829, for piecewise monotone functions (functions with a finite number of sections per period each of...

subsequence that converges in (X, <). Every monotone increasing sequence in X converges to a unique limit in X. Every monotone decreasing sequence in X converges...

1103/RevModPhys.50.221. J. Karamata. "Sur une inegalite relative aux fonctions convexes." Publ. Math. Univ. Belgrade 1, 145–158, 1932. G. H. Hardy, J...

fizyoloji * işlevbilim physiology physiologie fonksiyon * işlev function fonction fotokopi * tıpkıbasım photocopy photocopie garanti * güvence insurance...

Not all of them are completely monotone, i.e. d-monotone for all d ∈ N {\displaystyle d\in \mathbb {N} } or d-monotone for certain θ ∈ Θ {\displaystyle...

dealing mainly with harmonic progressions in the context of a general "monotonality". Both theories find part of their inspiration in the theories of Jean-Philippe...

from the intermediate value theorem that f {\displaystyle f} is strictly monotone. Consequently, f {\displaystyle f} maps intervals to intervals, so is an...

ISBN 978-0-691-08527-2. Fréchet, Maurice (1907), "Sur les ensembles de fonctions et les opérations linéaires", C. R. Acad. Sci. Paris, 144: 1414–1416....

\omega \in \Omega } . Since we have a probability measure, the integral is monotone with μ ( Ω ) = 1 {\displaystyle \mu (\Omega )=1} so that ∫ Ω φ ∘ g d μ...

For p < ∞ , {\displaystyle p<\infty ,} the Minkowski inequality and the monotone convergence theorem imply that ∫ ( ∑ n = 0 ∞ | u n | ) p d μ ≤ ( ∑ n =...

Invitation to combinatorial topology, 2003 Fonctions définies-positives et les fonctions complètement monotones; leurs applications au calcul des probabilités...

be calculated. At the end of the century, Lagrange in his Théorie des fonctions analytiques (1797) opined that the lack of rigour precluded further development...

theorem. Mathematics portal Analog signal processing Bernstein's theorem on monotone functions Continuous-repayment mortgage Hamburger moment problem Hardy–Littlewood...

10502. Bauschke, H.H., and Combettes, P.L. (2011). Convex analysis and monotone operator theory in Hilbert spaces. Springer.{{cite book}}: CS1 maint: multiple...