The Fubini Theorem

1978 ◽  
pp. 91-105
Author(s):  
Jan Mikusiński
Keyword(s):  
Fubini Theorem

scholarly journals A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral

2011 ◽  
Vol 9 (3) ◽  
pp. 283-304 ◽  
Author(s):  
A. Boccuto ◽  
D. Candeloro ◽  
A. R. Sambucini
Keyword(s):  
Type Theorem ◽  
Riesz Space ◽  
Fubini Theorem ◽  
Real Plane ◽  
Henstock Integral ◽  
Riesz Spaces

A Fubini-type theorem is proved, for the Kurzweil-Henstock integral of Riesz-space-valued functions defined on (not necessarily bounded) subrectangles of the “extended” real plane.

scholarly journals A Fubini theorem for iterated stochastic integrals

1978 ◽  
Vol 84 (1) ◽  
pp. 159-161 ◽  
Author(s):  
Marc A. Berger ◽  
Victor J. Mizel
Keyword(s):  
Fubini Theorem ◽  
Stochastic Integrals

An Unsymmetric Fubini Theorem

1984 ◽  
Vol 91 (2) ◽  
pp. 131-133 ◽  
Author(s):  
G. W. Johnson
Keyword(s):  
Fubini Theorem

The Fubini Theorem for Bornological Product Measures

2009 ◽  
Vol 54 (1-2) ◽  
pp. 65-73 ◽  
Author(s):  
Ján Haluška ◽  
Ondrej Hutník
Keyword(s):  
Fubini Theorem ◽  
Product Measures

An Unsymmetric Fubini Theorem

1984 ◽  
Vol 91 (2) ◽  
pp. 131 ◽  
Author(s):  
G. W. Johnson
Keyword(s):  
Fubini Theorem

scholarly journals Stability of reaction–diffusion systems with stochastic switching

2019 ◽  
Vol 24 (3) ◽  
pp. 315-331 ◽  
Author(s):  
Lijun Pan ◽  
Jinde Cao ◽  
Ahmed Alsaedi
Keyword(s):  
Direct Method ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Fubini Theorem ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Stochastic Switching ◽  
The Stability ◽  
Independent And Identically Distributed

In this paper, we investigate the stability for reaction systems with stochastic switching. Two types of switched models are considered: (i) Markov switching and (ii) independent and identically distributed switching. By means of the ergodic property of Markov chain, Dynkin formula and Fubini theorem, together with the Lyapunov direct method, some sufficient conditions are obtained to ensure that the zero solution of reaction–diffusion systems with Markov switching is almost surely exponential stable or exponentially stable in the mean square. By using Theorem 7.3 in [R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 2005], we also investigate the stability of reaction–diffusion systems with independent and identically distributed switching. Meanwhile, an example with simulations is provided to certify that the stochastic switching plays an essential role in the stability of systems.

Majorants in Variational Integration

1966 ◽  
Vol 18 ◽  
pp. 49-74 ◽  
Author(s):  
Ralph Henstock
Keyword(s):  
Euclidean Space ◽  
Fubini Theorem ◽  
Point Function ◽  
The Way

In Perron integration, majorants are usually functions of points. If the domain of definition is a Euclidean space of n dimensions, we can define a finitely additive n-dimensional majorant rectangle function by taking suitable differences of the majorant point function with respect to each of the n coordinates. The way is then open to a generalization, in that we need only suppose that the majorant rectangle function is finitely superadditive. Similarly, we need only suppose that a minorant rectangle function is finitely subadditive. These kinds of rectangle functions were used by J. Mařík (5) to prove the Fubini theorem for Perron integrals in Euclidean space of m + n dimensions. He also proved that for a function that is Perron, and absolutely Perron, integrable, the majorant and minorant rectangle functions can be taken to be finitely additive. As a result he posed the following problem.

Fubini Theorem For a Certain Type of Integral

1965 ◽  
Vol 17 ◽  
pp. 142-154
Author(s):  
Charles A. Hayes
Keyword(s):  
Product Space ◽  
Continuous Functions ◽  
Fubini Theorem ◽  
Riemann Integral ◽  
General Conditions

In (1), the writer defined a process of integration that leads to a kind of Riemann integral under certain rather general conditions. The purpose of this paper is to show how it is possible to use the process of integration of (1) to obtain integrals in a product space that satisfy a Fubini theorem. In this connection, we define a class of integrands that are the analogues of continuous functions in the product space, establish some of their properties, and finally arrive at a Fubini theorem for this class.

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