scholarly journals On the application of Fubini's theorem in the integration of functiions of two variables in a measure space

2013 ◽  
Vol 1 (2) ◽  
Author(s):  
'Bankole V Akinremi ◽  
Ubong Sam Idiong ◽  
Bridjet Akintewe ◽  
Kayode Samuel Famuagun
Keyword(s):  
Measure Space ◽  
Fubini’S Theorem ◽  
Fubini's Theorem

scholarly journals Fubini’s Theorem for Non-Negative or Non-Positive Functions

2018 ◽  
Vol 26 (1) ◽  
pp. 49-67
Author(s):  
Noboru Endou
Keyword(s):  
Integrable Function ◽  
Functional Space ◽  
The Other ◽  
Integration Theory ◽  
Fubini’S Theorem ◽  
Positive Functions ◽  
System 1 ◽  
Article 5 ◽  
Fubini's Theorem ◽  
Lebesgue Integration

Summary The goal of this article is to show Fubini’s theorem for non-negative or non-positive measurable functions [10], [2], [3], using the Mizar system [1], [9]. We formalized Fubini’s theorem in our previous article [5], but in that case we showed the Fubini’s theorem for measurable sets and it was not enough as the integral does not appear explicitly. On the other hand, the theorems obtained in this paper are more general and it can be easily extended to a general integrable function. Furthermore, it also can be easy to extend to functional space Lp [12]. It should be mentioned also that Hölzl and Heller [11] have introduced the Lebesgue integration theory in Isabelle/HOL and have proved Fubini’s theorem there.

The Wave Equation, Mixed Partial Derivatives, and Fubini's Theorem

2004 ◽  
Vol 111 (4) ◽  
pp. 340-347
Author(s):  
Asuman Aksoy ◽  
Mario Martelli
Keyword(s):  
Wave Equation ◽  
Partial Derivatives ◽  
Fubini’S Theorem ◽  
Fubini's Theorem

Fubini's Theorem for Ultraproducts of Noncommutative Lp-Spaces

2004 ◽  
Vol 56 (5) ◽  
pp. 983-1021 ◽  
Author(s):  
Marius Junge
Keyword(s):  
Von Neumann Algebras ◽  
Type Result ◽  
Von Neumann ◽  
Lp Spaces ◽  
Fubini’S Theorem ◽  
Image Position ◽  
Local Reflexivity ◽  
Fubini's Theorem

AbstractLet (ℳi)i∈I, be families of von Neumann algebras and be ultrafilters in I, J, respectively. Let 1 ≤ p < ∞ and n ∈ ℕ. Let x1,… ,xn in ΠLp(ℓi ) and y1,… ,yn in be bounded families. We show the following equalityFor p = 1 this Fubini type result is related to the local reflexivity of duals of C*-algebras. This fails for p = ∞.

Fubini's Theorem for Null Sets

1989 ◽  
Vol 96 (8) ◽  
pp. 718-721 ◽  
Author(s):  
Eric K. van Douwen
Keyword(s):  
Fubini’S Theorem ◽  
Fubini's Theorem
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