  We study Laurent polynomials in any number of variables that are sums of at
most $k$ monomials. We first show that the Mahler measure of such a polynomial
is at least $h/2^{k-2}$, where $h$ is the height of the polynomial. Next,
restricting to such polynomials having integer coefficients, we show that the
set of logarithmic Mahler measures of the elements of this restricted set is a
closed subset of the nonnegative real line, with $0$ being an isolated point of
the set.
  In the final section, we discuss the extent to which such an integer
polynomial of Mahler measure $1$ is determined by its $k$ coefficients.

Number Theory