Integroitavat

Integroitavat is a Finnish mathematical term used to describe objects that can be integrated, i.e., integrable, under a given theory of integration.

Form and use: It is derived from the verb integroida (to integrate). The form integroitava is the participial adjective; the plural integroitavat refers to several integrable items, for example integroitavat funktiot (integrable functions).

Contexts and criteria: In real analysis, an object is integroitava with respect to a particular integral if the integral exists and is finite. Under the Riemann integral, this typically requires the function to be bounded on a closed interval and have only a set of discontinuities of measure zero. Under the Lebesgue integral, a function is integroitava if the integral of its absolute value is finite (i.e., the function is Lebesgue integrable).

Examples and usage: Continuous functions on a closed interval are integroitavat for both Riemann and Lebesgue integration. In practice, texts may discuss integroitavat funktiot when listing which functions can be integrated, or when distinguishing between integrable and non-integrable cases in a given setting.

Notes: The term is common in Finnish-language mathematical literature; exact usage may vary by author or school. It serves as a concise way to refer to objects that satisfy the criteria needed for the chosen notion of integration.