Jiří Jarník

Another Perron type integration in n dimensions as an extension of integration of stepfunctions

AbstractFor a new Perron-type integral a concept of convergence is introduced such that the limit f of a sequence of integrable functions

A non absolutely convergent integral which admits transformation and can be used for integration on manifolds

f_k ,k \in \mathbb{N}

A new and more powerful concept of the PU-integral

is integrable and any integrable f is the limit of a sequence of stepfunctions

Perron-type integration on

g_k ,k \in \mathbb{N}

-dimensional intervals and its properties

.