Abstract
In this chapter, we recall well-known definitions and concepts. We state and prove Silverman–Toeplitz theorem and Schur’s theorem and then deduce Steinhaus theorem. A sequence space \(\Lambda _r\), \(r \ge 1\) being a fixed integer, is introduced, and we make a detailed study of the space \(\Lambda _r\), especially from the point of view of sequences of zeros and ones. We prove a Steinhaus type result involving the space \(\Lambda _r\), which improves Steinhaus theorem. Some more Steinhaus type theorems are also proved.
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Natarajan, P.N. (2017). General Summability Theory and Steinhaus Type Theorems. In: Classical Summability Theory. Springer, Singapore. https://doi.org/10.1007/978-981-10-4205-8_1
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DOI: https://doi.org/10.1007/978-981-10-4205-8_1
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