Note: Correction to "Note on a Limit Theorem"

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

Technical Note - A Limit Theorem on Subintervals of Interrenewal Times

Consider a renewal process {X,, n 2 1} for which there is defined an associated sequence of independent and identically distributed random variables {Bn, n 2 1 } such that Bn is the length of a subinterval of Xn. We show that when attention is restricted only to B-intervals, the asymptotic joint distribution of the residual life and total life of a B-interval is that of a renewal process genera...

Note on a Theorem Due to Borsuk

A Note on Goodman's Theorem

Goodman's theorem states that intuitionistic arithmetic in all nite types plus full choice, HA ! + AC, is conservative over rst-order intuitionistic arithmetic HA. We show that this result does not extend to various subsystems of HA ! , HA with restricted induction.

A Note on Tchakaloff’s Theorem

A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.