فهرست نشریات علمی دسترسی آزاد ایران

‎In this paper‎, ‎we introduce a gyrodistance on the gyrolinear space of functions (whose gyronorm is measurable) from a measure space to the Möbius disk $\mathbb{D}$‎. ‎The gyrodistance in question can be expressed in terms of a modification of the Lebesgue integral‎, ‎which we will call the Lebesgue gyrointegral‎. ‎The gyronormed space generated in this manner‎, ‎which we will call the $L^1$ gyrospace‎, ‎is similar to the familiar $L^1$ function space in many aspects‎. ‎We establish several properties of the latter‎, ‎showing that many of them mirror those of classical $L^1$ spaces‎. ‎Finally‎, ‎we show that the gyrodistance in question induces a metric topology on the $L^1$ gyrospace‎.