Generalized Limits in General Analysis

Generalized Limits in General Analysis.

In a previous paper of the same titlet I have developed the fundamental principles of a general theory which includes as particular instances the theories of Cesàro and Holder summability of divergent series and divergent integrals. I further made use of these fundamental principles to prove a general theorem which includes as special cases several important theorems in the above mentioned spec...

Generalized Limits in General Analysis , First Paper

The analogies that exist between infinite series and infinite integrals are well known and have frequently served to indicate the extension of a theorem or a method from one of these domains of investigation to the other. According to a principle of generalization that has been formulated by E. H. Moore, the presence of such analogies implies the existence of a general theory which includes the...

Generalized Covering Groups and Direct Limits

generalized covering groups and direct limits

Speed Limits in General Relativity

Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994) in the absence of exotic matter.