2. Convergence Theorem in Measurable Spaces In this section, we consider a measurable space (X, ), a sequence of measures on %, and a real-valued measurable nonnegative function f on X. 2.1 Fatou’s Lemma and Lebesgue’s Convergence Theorems for Measures We have the following result: ...
By a general method, based on weak convergence of transition probabilities, new infinite-dimensional Fatou lemmas are derived.Erik J BalderJournal of Mathematical Analysis and ApplicationsE.J. Balder, Fatou's lemma in infinite dimensions, J. Math. Anal. Appl. 136 (1988) 450-465....
Fatou’s Lemma for the Sequence of Random Sets L I Gao2m ing (Engineering co llege of the A rmed po lice Fo rce, Xi’an 710086) Abstract: Fatou’s lemma in the sense of weak convergence fo r set2valued condit ional expectat ion w ith ...
Majumdar, Weak sequential convergence in L1(µ, X) and an approxi- mate version of Fatou's lemma, J. Anal. Appl. 114 (1986), 569-573.M Ali Khan and Nobusumi Sagara. Weak sequential convergence in L1(µ, X) and an exact version of Fatou's lemma. Journal of Mathematical ...
weak convergencesetwise convergenceMarkov decision processThe classical Fatou lemma states that the lower limit of a sequence of integrals of functions is greater than or equal to the integral of the lower limit. It is known that Fatou's lemma for a sequence of weakly converging measures states ...
"Convergence in a dual space with applications to Fatou lemma", Adv. Math. Econ. 12, 23-69.C. Castaing and M. Saadoune, Convergences in a dual space with Applications to Fatou Lemma, Adv. Math. Econ. 12 (2009), 23-69.Castaing, C., Saadoune, M.: Convergences in a dual space...
Weak convergenceFatou's lemmaInverse momentsCrame´r's theoremBerry–Esse´en's boundSufficient conditions for convergence of monotone moments of weakly convergent random variables, concerning the rate of convergence, are given. They are often more convenient than the necessary and sufficient ...
M. A. Khan and M. Majumdar, Weak sequential convergence in L1(µ, X) and an approxi- mate version of Fatou's lemma, J. Anal. Appl. 114 (1986), 569-573.M Ali Khan and Nobusumi Sagara. Weak sequential convergence in L1(µ, X) and an exact version of Fatou's lemma. ...