sequences and series - Monotonically increasing vs Non-decreasing . . . Note that the Monotone Convergence Theorem applies regardless of whether the above interpretations: a non-decreasing (or strictly increasing) sequence converges if it is bounded above, and a non-increasing (or strictly decreasing) sequence converges if it is bounded below
monotone class theorem, proof - Mathematics Stack Exchange In words, it is a monotone class containing the algebra $\mathcal A$ Since $\mathcal M$ is the smallest monotone class containing $\mathcal A$, it must be contained in any other monotone class containing $\mathcal A$
Proof of the divergence of a monotonically increasing sequence Show that a divergent monotone increasing sequence converges to $+\infty$ in this sense I am having trouble understanding how to incorporate in my proof the fact that the sequence is monotonically increasing
Continuity of Probability Measure and monotonicity In every textbook or online paper I read, the proof of continuity of probability measure starts by assuming a monotone sequence of sets $(A_n)$ Or it assumes the $\\liminf A_n = \\limsup A_n$ But w