Ideály odvodené od lsc submier
Referujúci: M. Sleziak; semináre: 20.2., 27.2, 7.3
Stručný úvod o ideáloch odvodených od zdola polospojitých submier - základné vlastnosti submier a ideálov tvaru $\operatorname{Exh}(\phi)=\{A\subseteq\mathbb N; \|A\|_\phi = 0\}$ a $\operatorname{Fin}(\phi)=\{A\subseteq\mathbb N; \phi(A)<\infty\}$.
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Seminár LS 2017/18
Moderator: Martin Sleziak
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Martin Sleziak
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Re: Seminár LS 2017/18
Stieltjesov integrál
Referujúci: P. Letavaj (na seminároch od 14.3. do 2.5.)
Kapitola 23 z knihy A. C. M. van Rooij, W. H. Schikhof: A Second Course on Real Functions.
Referujúci: P. Letavaj (na seminároch od 14.3. do 2.5.)
Kapitola 23 z knihy A. C. M. van Rooij, W. H. Schikhof: A Second Course on Real Functions.
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Martin Sleziak
- Posts: 5524
- Joined: Mon Jan 02, 2012 5:25 pm
On partial limits of sequences
On partial limits of sequences (Ladislav Mišík, János T. Tóth)
Referujúci: L. Mišík; 11.4.
Abstract: The concept of a limit of a sequence is a basic concept in mathematical analysis. We analyse this concept in more details using another basic concept of analysis, the concept of measure on sets of positive integers. We dene a degree of convergence of a given sequence to a given point with respect to a chosen measure as a number in interval [0; 1]. We study its properties depending on properties of the chosen measure. It appears that standard limits and their known generalizations (convergence with respect to a filter or ideal) are special cases in our approach.
Referujúci: L. Mišík; 11.4.
Abstract: The concept of a limit of a sequence is a basic concept in mathematical analysis. We analyse this concept in more details using another basic concept of analysis, the concept of measure on sets of positive integers. We dene a degree of convergence of a given sequence to a given point with respect to a chosen measure as a number in interval [0; 1]. We study its properties depending on properties of the chosen measure. It appears that standard limits and their known generalizations (convergence with respect to a filter or ideal) are special cases in our approach.