A substitution theorem for Denjoy's integrals
نویسندگان
چکیده
منابع مشابه
a cauchy-schwarz type inequality for fuzzy integrals
نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.
15 صفحه اولComparison theorem for improper integrals
This is a complement to the comparison theorem for improper integrals in the textbook. The vanilla version presented in the textbook is good enough to solve some very easy examples and it becomes exponentially gory with the complexity of the integral. Fortunately it is not hard to refine the statement in the book, and turn it into a powerful tool to estimate the convergence of arbitrarily compl...
متن کاملVitali Convergence Theorem for Upper Integrals
It is shown that the Vitali convergence theorem remains valid for the -upper integral. Using this result we prove completeness of the space L( ) with respect to the k kp-upper norm for 1 p < 1 , describe convergence of its elements in terms of the space L( ) for 1 p < 1 , give a necessary and sufficient condition for a sequence from L( ) to converge in the k kp-upper norm to a function from L( ...
متن کاملThe First Mean Value Theorem for Integrals
For simplicity, we use the following convention: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, f , g are partial functions from X to R, and E is an element of S. One can prove the following three propositions: (1) If for every element x of X such that x ∈ dom f holds f(x) ≤ g(x), then g − f is non-negative. (2) For every set Y and for every partial function f from...
متن کاملIntegrals, partitions and MacMahon's Theorem
In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper is to extend that study in various ways. First, the relationship of partitions with no consecutive integers to a theorem of MacMahon and mock theta functions is explored independently. Secondly, we derive in a succinc...
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: Časopis pro pěstování matematiky
سال: 1956
ISSN: 0528-2195
DOI: 10.21136/cpm.1956.117225