Results 141 to 150 of about 1,716 (184)

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
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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.
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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
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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.
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Fubini theorem for F-valued integrals

Fuzzy Sets and Systems, 1994
Abstract In the paper, further investigations of set-valued integrals and F-valued integrals are carried out. After proving the Fubini theorem for set-valued integrals, the Fubini theorem for F-valued integrals is given. They are extensions of the classical Fubini theorem.
Deli Zhang, Caimei Guo
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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.
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Fubini's Theorem for Null Sets

The American Mathematical Monthly, 1989
(1989). Fubini's Theorem for Null Sets. The American Mathematical Monthly: Vol. 96, No. 8, pp. 718-721.
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Fubini-type theorem for anticipating integrals

Random Operators and Stochastic Equations, 1996
This paper is devoted to the proof of the following theorem: Let \(W_t\) be an \(r\)-dimensional Wiener process on a probability space \((\Omega,\mathfrak F,P)\). Let \((X,\mathcal X,\mu)\) be a measure space, \(\mu\) finite, and \(\varphi: X\times[0,1]\times\Omega\to\mathbb{R}^r\) an \(\mathcal X\otimes\mathfrak B([0,1])\otimes\mathfrak F\)-measurable
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Four counterexamples to the Fubini theorem

Mathematical Notes, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence, 2021
Lu Lu, Pengzhan Jin, Guofei Pang
exaly