Sentence examples for limit of sums from inspiring English sources

replaces tedious computations of the limit of sums of rectangular areas with a more easier way of finding an anti-derivative.

We show that for a finite, σ-finite von-Neumann algebra M and completely positive normal maps Φ, Ψ M → M, the correspondence associated to Φ, HΦ, is weakly contained in HΨ if and only if Ψ is a limit of sums of maps which are compositions of Φ with inner maps.

The integral of on is defined as the limit of the sums (if exists).

This triangular double integral is defined by single limit of double sums of triangularly divided areas.

They introduce the concept of integration along the interval as a limit of Cauchy sums.

The integral of on is defined by the limit of these sums (as ) if this limit exists.

Our triangular triple integral is possible to be formulated in the method of a single limit of triple sums.

The antisymmetric double integral here introduced demands only single limit of double sums of triangularly divided areas.

We end this section with a mean value result that comes in an obvious manner (taking into account that the integral is a limit of integral sums).

In Section 3, we develop a theory of a scalar triple product integral by a single limit of triple sums of tetrahedrally divided volumes and derive the divergence theorem in the 3D space.

In Section 4, we formulate a theory of an antisymmetric quadruple integral by a single limit of quadruple sums of hyper-triangularly divided hyper-volumes and derive the divergence theorem in the 4D time-space.