A substitute for Lebesgue’s bounded convergence theorem

A Substitute for Lebesgue's Bounded Convergence Theorem

1. P. R. Halmos, Introduction to Hubert space. New York, Chelsea, 1951. 2. M. Schreiber, On functions of contractions, to appear. 3. -, On absolutely continuous operators, to appear. 4. -, Unitary dilations of operators in Hubert space, Duke Math. J. vol. 23 (1956) pp. 579-594. 5. B. Sz.-Nagy, Sur les contractions de l'espace de Hubert, Seta Sei. Math. Szeged vol. 15 (1953) pp. 87-92. 6. B. Sz....

The Bounded Convergence Theorem for Riesz Space-Valued Choquet Integrals

The bounded convergence theorem on the Riesz space-valued Choquet integral is formalized for a sequence of measurable functions converging in measure and in distribution. 2010 Mathematics Subject Classification: Primary 28B15; Secondary 28A12, 28E10

A Concise, Elementary Proof of Arzelà's Bounded Convergence Theorem

Arzelà's Bounded Convergence Theorem (1885) states that if a sequence of Riemann integrable functions on a compact interval is uniformly bounded and has an integrable pointwise limit function, then the sequence of their integrals tends to the integral of the limit. It is a trivial consequence of measure theory; in particular, of the Dominated Convergence Theorem. However, denying oneself the ma...

A Convergence Theorem For Controlled . . .

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.