Multiply hyperharmonic functions (Q1357511)

The author studies multiply hyperharmonic functions, which are defined on the product of two harmonic spaces (in the sense of Constantinescu and Cornea) and are hyperharmonic in each variable. Earlier the theory was developed by \textit{K. GowriSankaran} [Nagoya Math. J. 28, 27-48 (1966; Zbl 0148.10501)] in Brelot spaces. Sheaf properties and the property of semicontinuity are studied. The axiom of completeness is proved with respect to the product of relatively compact sets.