Integral of Fine Computable functions and Walsh Fourier series

We dene the eective integrability of Finecomputable functions and eectivize some fundamental limit theorems in the theory of Lebesgue integral such as Bounded Con vergence Theorem and Dominated Convergence Theorem It is also proved that the WalshFourier coecients of an eectively integrable Finecomputable function form an E computable sequence of reals and converge eectively to zero The latter fact is the eectivization of WalshRiemannLebesgue Theorem The article is closed with the eec tive version of Dirichlets tes