Cover disposition for monitoring individuals in support surfaces of individuals, whereby said cover disposition comprises: - a textile material support presenting a top part (21, 22) adapted for covering at least part of upwards-oriented surface of an object that is adapted for supporting individuals; - a conducting textile disposition comprising a plurality of conducting textiles (31, 32) and associated with said textile material support; - a control device provided in energy conducting connection with said conduction textile disposition and with an energy source, whereby said textile material support presents a top part (21, 22) that comprises at least part of said conducting textile disposition, and wherein said textile material support is provided so that it can be arranged over said object so that said conducting textiles disposition is substantially retained relative to said object, at least with relation to movements along a longitudinal extension of said object, and wherein said control device and electric connections between the latter and said conducting textile disposition are associated with said textile material support so that they are retained thereon, and characterized in that said electrical connections are provided so that the placement of said textile material support upon said object does not require establishing any electrical connection, and the removal of said textile material support does not require disconnecting any electrical connection between said control device and said conducting textile disposition, by providing the textile material support with a general shape so as to enclose said object for supporting individuals inside thereof, and by providing said control device, energy source and all the energy conducting connections between said conducting textile disposition and said control device inside of the enclosure provided by said textile material support, so that said cover disposition does not present wire connections with the exterior thereof. - a textile material support presenting a top part (21, 22) adapted for covering at least part of upwards-oriented surface of an object that is adapted for supporting individuals; - a conducting textile disposition comprising a plurality of conducting textiles (31, 32) and associated with said textile material support; - a control device provided in energy conducting connection with said conduction textile disposition and with an energy source, whereby said textile material support presents a top part (21, 22) that comprises at least part of said conducting textile disposition, and wherein said textile material support is provided so that it can be arranged over said object so that said conducting textiles disposition is substantially retained relative to said object, at least with relation to movements along a longitudinal extension of said object, and wherein said control device and electric connections between the latter and said conducting textile disposition are associated with said textile material support so that they are retained thereon, and characterized in that said electrical connections are provided so that the placement of said textile material support upon said object does not require establishing any electrical connection, and the removal of said textile material support does not require disconnecting any electrical connection between said control device and said conducting textile disposition, by providing the textile material support with a general shape so as to enclose said object for supporting individuals inside thereof, and by providing said control device, energy source and all the energy conducting connections between said conducting textile disposition and said control device inside of the enclosure provided by said textile material support, so that said cover disposition does not present wire connections with the exterior thereof.