A fair distribution of public transport benefits is a commonly stated goal of agencies and operators of public transport. However, it is less complicated and costly to provide accessibility in some parts of cities and their surroundings than in other parts. Densely populated areas, and areas situated closer to the city center therefore often have higher public transport accessibility than remote or sparsely populated areas. Neglecting these realities results with an unrealistic assessment of equity in service provision and hampers their consideration when setting policy goals. In this study, we propose a framework for investigating equity in the distribution of accessibility, where the suggested goal is to provide residents with equal accessibility for equally dense and central areas. For the Stockholm County, we show that accessibility may seem to be distributed horizontally inequitable and vertically regressive. However, once controlling for how dense and close to the city center residents live, while still being horizontally inequitable the distribution of accessibility in Stockholm County is found progressive, i.e., benefiting those with lower incomes. We demonstrate the proposed method for the case of skip-stop train operations and find that it shifts our constructed accessibility measure toward a more horizontally inequitable and vertically progressive state. We conclude that our proposed method can be a potent way for public transport agencies to measure and concretize equity goals and evaluate policy changes.