Related papers: A Fubini rule for $\infty$-coends

We note that the Fubini theorem may be used to prove that an $L^1$ function is determined by its Fourier coefficients.

Let $f = f(z,t)$ be a function holomorphic in $z \in O \subseteq {\mathbb C}^d$ for fixed $t\in \Omega$ and measurable in $t$ for fixed $z$ and such that$z \mapsto f(z,\cdot)$ is bounded with values in$E := L_{p}(\Omega)$, $1\le p \le…

This short note shows a limiting behavior of integrals of some centered antipersistent stationary infinitely divisible moving averages as the compact integration domain in $d\ge 1$ dimensions extends to the whole positive quadrant…

We call a tensor functor $F:\mathcal{C}\to\mathcal{D}$ between finite tensor categories $\otimes$-Frobenius if its left and right adjoints are isomorphic as $\mathcal{C}$-bimodule functors. We give several characterizations of this notion…

The classical Fubini theorem asserts that the multiple integral is equal to the repeated one for any integrable function on a product measure space. In this paper, we derive an asymptotic variant of the Fubini theorem for maps into…

We answer the question to what extent homotopy (co)limits in categories with weak equivalences allow for a Fubini-type interchange law. The main obstacle is that we do not assume our categories with weak equivalences to come equipped with a…

Let the function $f: \bar{\R}^2_+ \to \C$ be such that $f\in L^1_{\loc} (\bar{\R}^2_+)$. We investigate the convergence behavior of the double integral $$\int^A_0 \int^B_0 f(u,v) du dv \quad {\rm as} \quad A,B \to \infty,\leqno(*)$$ where…

In this paper we evaluate sums and integrals of products of Fubini polynomials and have new explicit formulas for Fubini polynomials and numbers. As a consequence of these results new explicit formulas for p-Bernoulli numbers and…

We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit formulas, parity, asymptotics and determinantal…

We show how dinaturality plays a central role in the interpretation of directed type theory where types are interpreted as (1-)categories and directed equality is represented by $\hom$-functors. We present a general elimination principle…

We prove an abstract Fubini-type theorem in the context of monoidal and enriched category theory, and as a corollary we establish a Fubini theorem for integrals on arbitrary convergence spaces that generalizes (and entails) the classical…

We extend the formalism of I to a global setting for which a theorem on fiber integrals and a Fubini theorem are obtained. We compare our formalism to the previous constructions of motivic integration in the geometric and arithmetic cases.

Let $C\subseteq M$ be stably embedded in a structure $\cM=(M;\dots)$. We consider {\em Fubini measures} on the subcategory $\Def(C)$ of the category $\Def(\cM)$ of definable sets in $\cM$, with ``Fubini" signaling good behaviour in…

The classic stochastic Fubini theorem says that if one stochastically integrates with respect to a semimartingale $S$ an $\eta(dz)$-mixture of $z$-parametrized integrands $\psi^z$, the result is just the $\eta(dz)$-mixture of the individual…

In this short note we show that under very mild conditions on a functor between exact categories $F:\mathcal{D}\rightarrow\mathcal{E}$ it is possible to derive $F$ at the level of unbounded complexes. We also give applications to deriving…

We show that in the functional integral formalism of U(1) gauge field theory some formal manipulation such as interchange of order of integration can yield erroneous results. The example studied is analysed by Fubini theorem.

For a full subcategory B of a unital A_infinity-category C a quotient unital A_infinity-category `C/B' is defined. For differential graded categories such quotient is constructed by V.Drinfeld. Our construction is explicit and uses freely…

In this paper, we will prove Fubini type theorems for the strong McShane and strong Henstock-Kurzweil integrals of Banach spaces valued functions defined on a closed non-degenerate interval $[a,b] =[a_{1}, b_{1}] \times [a_{2}, b_{2}]…

In this paper, we investigate the umbral representation of the Fubini polynomials $F_{x}^{n}:=F_{n}(x)$ to derive some properties involving these polynomials. For any prime number $p$ and any polynomial $f$ with integer coefficients, we…

Euler calculus is based on integrating simple functions with respect to the Euler characteristic. This paper makes the case for extending Euler calculus to continuous integrands by integrating with respect to (Gaussian) curvature. This…