Results 171 to 180 of about 624,774 (227)

Fubini Theorems for Capacities

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2016
Capacity plays an important role in many areas. A capacity is usually studied under the assumption that it is concave (or convex). In this paper, we perform a further investigation on the Fubini Theorems for concave (or convex) capacities given by Ghirardato (1997) and Chateauneuf and Lefort (2008). We extend Fubini Theorems for capacities to a larger
openaire   +2 more sources

The fubini theorems of stochastic measures

Acta Mathematicae Applicatae Sinica, 1988
Suppose that (S,\(\Sigma)\) is a measurable space, E a Banach space, and Z a vector measure on \(\Sigma\) with values in the dual E' of E. If \(f: S\to E\) is a simple function of the form \(f=\sum^{n}_{i=1}x_ i 1_{A_ i}\) \((x_ i\in E\), \(A_ i\in \Sigma\) disjoint), it is natural to define the integral of f relative to Z by \[ \int f dZ:=\sum^{n}_{i ...
Jiang, Tao, Xiong, Zhengxin, Chen, Peide
openaire   +1 more source

Cartan-Fubini Type Extension Theorems

Acta Mathematica Vietnamica, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Fubini’s Theorem

1971
Linear Lebesgue measure is defined by covering sequences of intervals, and plane measure by covering sequences of rectangles. We shall now consider how these measures are related to each other. It is clear what kind of answer we should expect. In elementary calculus we learn to compute the area between the graphs of two functions f ≦ g by the formula
openaire   +1 more source

Fubini‐type theorems for general measure constructions

Mathematika, 2000
Summary: Methods are used from descriptive set theory to derive Fubini-like results for the very general Method I and Method II (outer) measure constructions. Such constructions, which often lead to non-\(\sigma\)-finite measures, include Carathéodory and Hausdorff-type measures.
Falconer, K. J., Mauldin, R. Daniel
openaire   +2 more sources

Fubini’s Theorem and Tonelli’s Theorem

1997
Abstract This chapter presents two theorems which allow us to relate the integral on JR with the integral on ℝk for k > l and to evaluate and manipulate higher dimensional integrals. These theorems are attributed to Fubini and Tonelli, whose names sound rather appropriately like those of a conjuring act.
openaire   +1 more source

FUBINI'S THEOREM FOR VECTOR-VALUED MEASURES

Mathematics of the USSR-Sbornik, 1991
In der Arbeit werden zwei Sätze bewiesen, die dem Fubinischen Satz ähnlich sind. Satz 1. Es sei \(X\) ein separierter topologischer Raum, \(\Sigma_ X\) eine Borelsche \(\sigma\)-Algebra, \(\mu\) ein Radonsches Maß. Ferner sei \(\nu\mu\) ein \(\sigma\)-beschränktes Maß und \(f:Z\to L(B,F)\) eine \(\nu\mu\) integrierbare Funktion. Dann gilt: Die Funktion
openaire   +2 more sources

Fubini-Tonelli theorems with local integrals

Acta Mathematica Hungarica, 1996
New integrability criteria of the integration in the abstract Riemann sense are established using a notion of measurability in the sense of Stone. A Fubini theorem and a Tonelli theorem are also stated for the abstract Riemann integral.
de Amo, E., Díaz Carrillo, M.
openaire   +2 more sources

A Note on Fubini's Theorem

The American Mathematical Monthly, 1993
does not exist in the Riemann sense. Gelbaum and Olmsted give two examples of such functions in "Counterexamples in Analysis (Holden-Day Inc.)". The first one is the characteristic function of a subset A of the unit square [0, 1] x [0, 1] that is dense in the unit square and such that every vertical or horizontal line meets A in only one point.
openaire   +1 more source

Stochastic Fubini Theorem for Jump Noises in Banach Spaces

Acta Mathematica Sinica. English series, 2020
Jia Zhu, Wei Liu
semanticscholar   +1 more source