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dc.contributor.authorHorbaczewska, Grażyna
dc.contributor.authorKarasińska, Aleksandra
dc.contributor.authorWagner-Bojakowska, Elżbieta
dc.contributor.editorFilipczak, Małgorzata
dc.contributor.editorWagner-Bojakowska, Elżbieta
dc.identifier.citationHorbaczewska G., Karasińska A., Wagner-Bojakowska E., Properties of the σ - ideal of microscopic sets, [w:] Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński, Filipczak M., Wagner-Bojakowska E. (red.), Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013, s. 325-343, doi: 10.18778/7525-971-1.20pl_PL
dc.description.sponsorshipUdostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Wiedza Edukacja Rozwój; nr umowy: POWER.03.05.00-00-Z092/17-00.pl_PL
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl_PL
dc.relation.ispartofFilipczak M., Wagner-Bojakowska E. (red.), Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński, Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013;
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe*
dc.subjectmicroscopic setspl_PL
dc.subjectnull setspl_PL
dc.subjectnegligible setspl_PL
dc.subjectCantor-type setspl_PL
dc.subjectcomparison of σ-idealspl_PL
dc.subjectcomparison of σ-fieldspl_PL
dc.titleProperties of the σ - ideal of microscopic setspl_PL
dc.typeBook chapterpl_PL
dc.contributor.authorAffiliationŁódź University, Faculty of Mathematics and Computer Sciencepl_PL
dc.contributor.authorAffiliationŁódź University, Faculty of Mathematics and Computer Sciencepl_PL
dc.contributor.authorAffiliationŁódź University, Faculty of Mathematics and Computer Sciencepl_PL
dc.referencesJ. Appell, Insiemi ed operatori "piccoli" in analisi funzionale, Rend. Ist. Mat. Univ. Trieste 33 (2001), 127–199.pl_PL
dc.referencesJ. Appell, A short story on microscopic sets, Atti. Sem. Mat. Fis. Univ. Modena Reggio Emilia 52 (2004), 229-233.pl_PL
dc.referencesJ. Appell, E. D’Aniello, M. Väth, Some remarks on small sets, Ric. Mat. 50 (2001), 255–274.pl_PL
dc.referencesM. Balcerzak, A generalisation of the theorem of Mauldin, Comment. Math. Univ. Carolin. 26, (1985), 209-220.pl_PL
dc.referencesM. Balcerzak, Can ideals without ccc be interesting?, Topology Appl. 55 (1994), 251–260.pl_PL
dc.referencesM. Balcerzak, Classification of σ-ideals, Math. Slovaca 37, no 1 (1987), 63–70.pl_PL
dc.referencesM. Balcerzak, On Borel sets modulo a σ-ideal, Demonstratio Math. 29 (2), (1996), 309–316.pl_PL
dc.referencesM. Balcerzak, J. E. Baumgartner, J. Hejduk, On certain σ-ideals of sets, Real Anal. Exchange 14, (1988–89), 447–453.pl_PL
dc.referencesT. Bartoszyński, H. Judah, Set theory: On the Structure of the Real Line, A. K. Peters, Ltd., Wellesley, MA, 1995.pl_PL
dc.referencesA. S. Besicovitch, An approximation in measure to Borel sets by Fσ -sets, Journal London Math. Soc. 29 (1954), 382–383.pl_PL
dc.referencesE. Borel, Les Eléments de la théorie des ensembles, Albin Michel, Paris, 1949.pl_PL
dc.referencesA. M. Bruckner, J. B. Bruckner, B. S. Thomson, Real Analysis, Prentice-Hall, Upper Saddle River, New Jersey 07458, 1997.pl_PL
dc.referencesJ. Cichoń, A. Kharazishvili, A. Węglorz, Subsets of the Real Line, Wydawnictwo Uniwersytetu Łódzkiego, 1995.pl_PL
dc.referencesP. Erdös, Some remarks on set theory, Ann. Math. 44 (2) (1943), 643–646.pl_PL
dc.referencesM. Filipczak, E. Wagner-Bojakowska, Remarks on small sets on the real line, Tatra Mt. Math. Publ. 42 (2009), 73–80.pl_PL
dc.referencesJ. Foran, P. D. Humke, Some set theoretic properties of σ-porous sets, Real Anal. Exchange 6 (1980-81), 114–119.pl_PL
dc.referencesM. Frechet, Les probabilites nulles et la rarefaction, Ann. scient. Ec. Norm. Sup., 30serie, 80 (1963), 139–172.pl_PL
dc.referencesG. Horbaczewska, E. Wagner-Bojakowska, Some kinds of convergence with respect to small sets, Reports on Real Analysis, Conference at Rowy (2003), 88–97.pl_PL
dc.referencesG. Ivanova, E. Wagner-Bojakowska, On some modification of Darboux property, Math. Slovaca (to appear).pl_PL
dc.referencesW. Just, C. Laflamme, Classifying measure zero sets with respect to their open covers, Trans. Amer. Math. Soc. 321, (1990), 621–645.pl_PL
dc.referencesA. Karasińska, W. Poreda, E. Wagner-Bojakowska, Duality Principle for microscopic sets in monograph Real Functions, Density Topology and Related Topics, Łódź University Press, 2011, 83–87.pl_PL
dc.referencesA. Karasińska, E. Wagner-Bojakowska, Nowhere monotone functions and microscopic sets Acta Math. Hungar. 120 (3) (2008), 235–248.pl_PL
dc.referencesA. Karasińska, E. Wagner-Bojakowska, Homeomorphisms of linear and planar sets of the first category into microscopic sets, Topology Appl. 159 (7) (2012), 1894– 1898.pl_PL
dc.referencesA. Karasińska, E. Wagner-Bojakowska, Microscopic and strongly microscopic sets on the plane. Fubini Theorem and Fubini property, Demonstratio Math. (to appear).pl_PL
dc.referencesC. Laflamme, A few σ-ideals of measure zero sets related to their covers, Real Anal. Exchange 17 (1991–92), 362–370.pl_PL
dc.referencesA. W. Miller, Special subsets of the real line In: Kunen K., Vaughan J.E. (Eds.), Handbook of Set-theoretic Topology, Elsevier, North Holland, Amsterdam, 1984, 201–233.pl_PL
dc.referencesJ. C. Oxtoby, Measure and Category, Springer - Verlag New York Heidelberg Berlin, 1980.pl_PL
dc.referencesS. Piccard, Sur les ensembles de distance, Mémoires Neuchatel Université, 1938–39.pl_PL
dc.referencesW. Sierpiński, Sur la dualité entre la première catégorie et la mesure nulle, Fund. Math. 22 (1934), 276–280.pl_PL
dc.referencesH. Steinhaus, Sur les distances des points dans les ensembles de mesure positive, Fund. Math. 1 (1920), 93–104.pl_PL
dc.referencesL. Zajíček, Porosity and σ-porosity, Real Anal. Exchange 13 (2) (1987-88), 314– 350.pl_PL
dc.referencesO. Zindulka, Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps, Fund. Math. 218 (2012), 95–119.pl_PL

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