Kempisty's theorem for the integral product quasicontinuity

• Autorzy: Zbigniew Grande
• Języki publikacji: EN

Abstrakty

EN

A function f: ℝⁿ → ℝ satisfies the condition $Q_{i}(x)$ (resp. $Q_{s}(x)$, $Q_{o}(x)$) at a point x if for each real r > 0 and for each set U ∋ x open in the Euclidean topology of ℝⁿ (resp. strong density topology, ordinary density topology) there is an open set I such that I ∩ U ≠ ∅ and $|(1/μ (U∩I)) ∫_{U∩I} f(t)dt - f(x)| < r$. Kempisty's theorem concerning the product quasicontinuity is investigated for the above notions.

Kategorie tematyczne

• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 26B05: Continuity and differentiation questions
• 26A03: Foundations: limits and generalizations, elementary topology of the line

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 2
• Strony: 257-264

Daty

wydano

2006

Twórcy

autor

Zbigniew Grande

• Institute of Mathematics, Kazimierz Wielki University, Plac Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

Identyfikatory

DOI

10.4064/cm106-2-6