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<p>We explore the lattice properties inherited by the space of Bochner integrable functions, denoted by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^1(\mu ,E)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, from a Banach lattice <i>E</i>. The aim of this work is to provide a generalization of classic convergence theorems for the Bochner integral. We will specifically focus on the monotone convergence theorem and Fatou’s lemma.</p>

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Convergence theorems in the space of Bochner integrable functions valued in a Banach space

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Celia Avalos-Ramos,
  • Saúl René Márquez-Sosa

摘要

We explore the lattice properties inherited by the space of Bochner integrable functions, denoted by \(L^1(\mu ,E)\) L 1 ( μ , E ) , from a Banach lattice E. The aim of this work is to provide a generalization of classic convergence theorems for the Bochner integral. We will specifically focus on the monotone convergence theorem and Fatou’s lemma.