3 окт. 2012 г. · Wikipedia claims, if σ-finite the Dominated convergence theorem is still true when pointwise convergence is replaced by convergence in measure.

29 нояб. 2020 г. · 1. '@Maths1999_ There is a version of DCT for convergence in measure. If you use that then there is no need for going to second subsequence ...

8 мая 2020 г. · You have shown that if (fn) converges to f in measure, then there exists some subsequence (fnk) that converges to f in Lp.

20 окт. 2019 г. · Suppose that a sequence of measurable functions hn converges to h in measure. Assume h is integrable and there exists a finite constant K ...

15 мая 2015 г. · The monotone convergence theorem holds, if the hypothesis of almost everywhere convergence is replaced by convergence in measure.

16 июл. 2015 г. · A Dominated Convergence Theorem for Product Measurable Functions · 0 · Am I applying the Dominated Convergence Test correctly in this example?

10 июн. 2019 г. · Show activity on this post. The DCT states that if fn is a sequence of measurable functions and if there exist g∈L such that |fn|≤g and fn→f ...

24 нояб. 2022 г. · A exercise in a measure textbook I own asks: Give an example to show that the conclusion of the dominated convergence theorem (DCT) may ...

12 окт. 2017 г. · It approaches 0 almost everywhere, but it is not bounded almost everywhere · You can however use DCT to evaluate the limit along the subsequence ...

2 окт. 2012 г. · Using the triangle inequality to determine bounds for DCT applications is a very common tool, so it is good to practice these types of problems.