On Pettis integrability of translations of functions in L^[infinity]

• Autorzy: Michalak A.
• Języki publikacji: EN

Abstrakty

EN

Let K be a compact Hausdorff space, mi a positive Radon measure on K, and let G be a compact group with the Haar measure lambda. We consider properties of the following generalization of translations on groups: we associate with every bounded to mi x R[lambda]- measurable function f : K x G --> C the function T[sub f] : G --> L^[infinity] (mi x R[lambda]) given by T[sub f](t) = f[sub t] where f[sub t](r, s) = f (r, ts). We show that if K and G are metrizable and the class of f [belongs to] L^[infinity](mi x R[lambda]) contains a function g such that lambda({t [belongs to] G : (r, t) is a point of discontinuity of g}) = 0 for every r [belongs to] supp(mi), then T[sub f] is Pettis integrable with respect to lambda.

Słowa kluczowe

EN

Pettis integral; translations on compact groups

PL

całka Pettisa; translacja na grupach zwartych

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 2
• Strony: 113--119
• Opis fizyczny: Bibliogr. 7 poz.,

Twórcy

autor

Michalak A.

• Faculty of Mathematics and Computer Sciences, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland,