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2006•Journal of Hanshan Normal UniversityRequires access

LSRS Convergence Theorem of Mcshane Integral

Wei Li

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Abstract

This paper gains the convergence theorem (Theorem 1) of locally small Riemann sum of Mcshane integral, which utilizes the properties of locally small Riemann sum of function(LSRS) and uniformly locally small Riemann sum of sequence of functions(ULSRS). Then it is proved that Lebesgue integral dominated convergence theorem is a corollary of Theorem 1 in Theorem 2.

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What this paper is about

This paper gains the convergence theorem (Theorem 1) of locally small Riemann sum of Mcshane integral, which utilizes the properties of locally small Riemann sum of function(LSRS) and uniformly locally small Riemann sum of sequence of functions(ULSRS). Then it is proved that Lebesgue integral dominated convergence theorem is a corollary of Theorem 1 in Theorem 2.

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Available abstract

This paper gains the convergence theorem (Theorem 1) of locally small Riemann sum of Mcshane integral, which utilizes the properties of locally small Riemann sum of function(LSRS) and uniformly locally small Riemann sum of sequence of functions(ULSRS). Then it is proved that Lebesgue integral dominated convergence theorem is a corollary of Theorem 1 in Theorem 2.

Key concepts: Lebesgue integration, Dominated convergence theorem, Mathematics, Corollary, Riemann sum, Riemann integral, Convergence (economics), Fundamental theorem of calculus

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