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Mat. Sb., 2000, Volume 191, Number 12, Pages 123–140 (Mi msb531)  

This article is cited in 4 scientific papers (total in 4 papers)

Theorems on representation of functions by series

K. S. Kazariana, D. Watermanb

a Universidad Autonoma de Madrid
b Syracuse University

Abstract: It is shown that if a system $\Phi$ of functions is such that each measurable function that is finite almost everywhere can be represented by a $\Phi$-series convergent in measure, then the same is true for measurable functions that can be equal to plus infinity or minus infinity on sets of positive measure.

DOI: https://doi.org/10.4213/sm531

Full text: PDF file (284 kB)
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English version:
Sbornik: Mathematics, 2000, 191:12, 1873–1889

Bibliographic databases:

UDC: 517.51
MSC: 42C15, 40A30
Received: 24.02.2000

Citation: K. S. Kazarian, D. Waterman, “Theorems on representation of functions by series”, Mat. Sb., 191:12 (2000), 123–140; Sb. Math., 191:12 (2000), 1873–1889

Citation in format AMSBIB
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\paper Theorems on representation of functions by series
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\pages 123--140
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kazarian K., “A complete orthonormal system of divergence”, C. R. Math. Acad. Sci. Paris, 337:2 (2003), 85–88  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. Kazarian K., “The zero-one law for a complete orthonormal system”, C. R. Math. Acad. Sci. Paris, 339:5 (2004), 335–337  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. Kazarian K.S., “A complete orthonormal system of divergence”, J. Funct. Anal., 214:2 (2004), 284–311  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. K. S. Kazarian, “On the Ul'yanov problem”, Sb. Math., 197:12 (2006), 1805–1826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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