Convergence of monotone nets - Mathematics Stack Exchange In sequences of real numbers, we have a monotone convergence result: If an+1 ≥ an a n + 1 ≥ a n and bounded, then an a n converges to it's supremum The proof seems to work also in the net case My question is given that our net is not into the reals but a general linearly ordered space, and it is a monotonically increasing and bounded, can we say that such always converges in the order
Monotone convergence theorem of random variables and its example where E is expectation I read about a example using the Monotone Convergence Theorem on the text book and found some problems The example is stated as follows: Assume r v X is non-negative, and denote μ = EX μ = E X, define sequence of r v :
logic - Meaning of Monotone in Monotone Disjunction - Mathematics . . . Disjunction is a monotone operator, because if you have a disjunction A ∨ B A ∨ B and change one of the inputs from one truth value to the other (while keeping the other one constant) then the truth value of the entire disjunction cannot possibly change in the opposite direction
A monotone convergence theorem for nets in Reed and Simon, Vol. I This is not quite your classical monotone convergence theorem, as it requires each fα to be continuous This is necessary in order to rule out common counter-examples (see, for instance, this question or these answers) to the statement of the dominated convergence theorem for nets instead of sequences I could try adapting a usual proof for
Strong convexity and strong monotonicity of the sub-differential Moreover this is a counter example to the original question because if the original question had a positive answer, would have a strongly monotone subgradient hence be strictly convex and its conjugate would be