Extension of the continuity theorems of Lebesgue integration

DOI10.14321/REALANALEXCH.48.1.1643688157OpenAlexW4321768069WikidataQ123154520 ScholiaQ123154520MaRDI QIDQ6046602

Suman Majumdar

Publication date: 11 May 2023

Published in: Real Analysis Exchange (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/real-analysis-exchange/volume-48/issue-1/Extension-of-the-Continuity-Theorems-of-Lebesgue-Integration/10.14321/realanalexch.48.1.1643688157.full

zbMATH Keywords

Fatou's lemmadominated convergence theoremmonotone convergence theoremLevy continuity theoremcountably accessible directed setRiesz's characterization of \(\mathcal{L}_p\) convergenceScheffe's theorem

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Integration with respect to measures and other set functions (28A25) Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Convergence of probability measures (60B10)

Related Items (1)

Equivalence of asymptotic normality of the two sample pivot and the vector of standardized sample means

Cites Work

• Why the theorem of Scheffé should be rather called a theorem of Riesz
• Weak convergence and empirical processes. With applications to statistics
• Central limit theorems revisited
• Two applications of nets
• Countable and Net Convergence
• Shorter Notes: Mean Convergence in L p Spaces
• A Useful Convergence Theorem for Probability Distributions
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