Using the SEST telescope we have mapped the lambda 1.3-mm and 2.9-mm c
ontinuum emission around Eta Carinae (eta Car), the peculiar star belo
nging to the open cluster Trumpler 16 in the Carina Nebula. The maps a
re dominated by a central source whose position coincides with eta Car
. Extended millimeter continuum emission is detected both at lambda 1.
3 and 2.9-mm. This emission traces the optically thin free-free emissi
on from the gas ionized by the nearby massive luminous stars of Trumpl
er 16. In 1992, the flux densities of eta Car were 15.8+/-1.9 Jy at la
mbda 1.3-mm and 4.9+/-0.7Jy at 2.9-mm. From an analysis of the spectru
m from the near-infrared to the decimeter radio range, we show that th
e millimeter emission of eta Car is dominated by thermal emission from
the ionized stellar wind. The infrared emission is dominated by dust
radiation with temperatures ranging from 200 to 400 K. The total lumin
osity is L(IR) = 5 10(6) L.. Based on the millimeter flux densities me
asured in 1992, we derive a mass-loss rate of similar to 2.4 10(-3) M.
yr(-1). Measurements obtained during the time interval from 1991 to 19
94 indicate strong flux density variations at both millimeter waveleng
ths. We suggest that these variations are related to episodic shell ej
ections leading to variations in the degree of ionization in the wind
of eta Car.