Abstract
Let \(I:=\bigcup_{i=1}^{\infty}\{2^{m_{i}}<n\leq 2^{m_{i}+1}\}\) , where \(m_{i}\) is some increasing sequence of natural numbers. It is proved, if partial sums \(\sum_{k=1}^{n}a_{k}\chi_{k}(x)\) , \(n\in I\) , of Haar series everywhere converge to everywhere finite integrable function \(f\) , then that series is Fourier–Haar series of the function \(f\) .
