An $$L^0 (\mathcal{F},\mathbb{R})$$ -valued function’s intermediate value theorem and its applications to random uniform convexity
نویسندگان
چکیده
منابع مشابه
An Intermediate Value Theorem for the Arboricities
Let G be a graph. The vertex edge arboricity of G denoted by a G a1 G is the minimum number of subsets into which the vertex edge set of G can be partitioned so that each subset induces an acyclic subgraph. Let d be a graphical sequence and let R d be the class of realizations of d. We prove that if π ∈ {a, a1}, then there exist integers x π and y π such that d has a realization G with π G z if...
متن کاملA differential intermediate value theorem
In this survey paper, we outline the proof of a recent differential intermediate value theorem for transseries. Transseries are a generalization of power series with real coefficients, in which one allows the recursive appearance of exponentials and logarithms. Denoting by T the field of transseries, the intermediate value theorem states that for any differential polynomials P with coefficients...
متن کاملFan-KKM Theorem in Minimal Vector Spaces and its Applications
In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.
متن کاملPerhaps the Intermediate Value Theorem
In the context of intuitionistic real analysis, we introduce the set F consisting of all continuous functions φ from [0, 1] to R such that φ(0) = 0 and φ(1) = 1. We let I0 be the set of all φ in F for which we may find x in [0, 1] such that φ(x) = 12 . It is well-known that there are functions in F that we can not prove to belong to I0, and that, with the help of Brouwer’s Continuity Principle ...
متن کاملLaplace Transform of Distribution-valued Functions and Its Applications
1. Notation and notions We repeat some definitions and facts, we need in our exposition but for special case. Let Q be an open set belonging to Rn. By D(Q) we denote the space {φ ∈ C∞(Q); suppφ ⊂ Kφ}, Kφ is a compact set in Q which depends on φ. D′(Q) is the space of continuous linear functionals on D(Q) the space of distributions. Every f ∈ Lloc(Q) defines a distribution, called regular distri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2011
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-011-0367-2