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 Green Line: The monotone class generated by $\mathcal A$, which we call $\mathcal M$, is the smallest monotone class containing $\mathcal A$, meaning no other monotone class containing $\mathcal A$ is properly contained inside $\mathcal M$
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
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