Fine-computable Functions on the Unit Square and their Integral

Takakazu Mori (Kyoto Sangyo University, Japan)

Mariko Yasugi (Kyoto Sangyo University, Japan)

Yoshiki Tsujii (Kyoto Sangyo University, Japan)

Abstract: We discuss the integral and Fubini's Theorem for a Fine-computable function F(x, y) on the upper-right open unit square [0, 1) x [0,1). The core objective is Fine-computability of f(x) = ∫ _[0,1) F(x,y)dy as a function of x ∈ [0,1).

Keywords: Fine-computable function, Fubini's Theorem, integral operator

Categories: F.0, F.m